Short Version:
Maybe P is overwhelmed by bookkeeping and it's distracting him from situational awareness. Help him make a mechanically very simple character without fiddly bits or conditionals to keep track of, so he can focus on making good choices rather than having good bookkeeping. Invite the other players to support P with advice and by being good role models for the behaviour he's trying to cultivate.
Long form answer, with rambling and details.
Back in my very first RPG ever--and also my first time as a GM--I had a player whose poor choices got him repeatedly killed. Let's call him Q.
Q knew the rules and mechanics quite well, but had a very hard time applying them intelligently to whatever situation he found himself in (like forgetting to heal himself as a cleric). Even more than that, though, was his role-playing: he really really liked to role-play his characters, but that got him in trouble because when Q got deep into his character's internal motives the PC would lose common sense and perspective about the surrounding context of his actions.
It got bad. Really bad. Q's second character was killed by the party for betraying them (he had a conversation about his friends over tea with a "nice" lady). At that point I shared Making the Tough Decisions with the group. He studied it carefully, had intense discussions with me about it... and as a direct result his fourth character perished of untempered curiosity: the characterisation "very curious" overcame the common sense "half these items are cursed and my friends are begging me to stop," until the pile of treasure he was investigating yielded up a lethal curse.
After that session I took Q aside and we talked. He knew he had a problem, and he was trying to "get better," but he needed help. I'd noticed that all his PCs so far were mechanically complicated and required in-game bookkeeping: advanced casters and races with lots of conditional features and spell-like abilities to keep track of. So we hatched the simplest possible character build: nothing to keep track of. No "if you're flanking, X also happens," no spells, no per-day abilities. If his character sheet said he could do a thing, he could always do it.
We wound up with a kind of Indiana Jones flavoured skillmonkey (a rogue chassis with homebrew mods to replace things like sneak attack because tracking whether you can deal that extra damage was beyond what we wanted for the build). He wasn't optimised in the traditional sense--but since another PC in the party had straight levels in the NPC Expert class, that wasn't an issue in keeping him relevant in the group. Instead he was optimised for what Q needed: a simple no-bookkeeping character to let him focus on situational awareness and making good choices.
At the end of each session he'd hang back --along with any other players who wanted to-- and we'd reflect on the game: what worked, what didn't. We'd consult (and if necessary research) and come up with what to make sure we did again, and what we'd change next time. (I've since found that any game I run which has some form of this "reflect and plan" dynamic after every session is improved by it.)
In tandem with another player rising to the challenge and being a kind of "teach by example" role model, it worked. A year later Q was successfully running complicated wizard builds with great party dynamics and great depth of character. He was a real joy to work with, and all he needed was to wade in at the shallow end of the bookkeeping pool instead of jumping into the deepest part head-first.
nota bene: My players have tended to treat the group dynamic as one of table-level cooperation between friends. However much their characters may be rivals, at the table they collaborate to tell the best stories, and I'm also one of the collaborators. In groups where players and/or the GM act as rivals at the table level of things, I'm not sure how much my experience will be useful. It sounds like your whole group isn't really on the same page in terms of their desired gameplay experience, and communication isn't really strong. Working on improving the "friends at the table" level of things might help your game in a number of ways.
Giant in the Playground's Increasing Size, Effective Size, Unarmed Damage, Reach thread is of some limited utility.
Minmaxboard's Grappling Handbook, Hulkamania is runnin' wild, is of somewhat more use.
From your current position, I suggest the following.
Option 1: Sorcerer
No, really. Enlarge Person as a spell gives you +5 to your grapple modifier. It comes in a cheap wand at your level. Babau Slime increases your grapple damage with a bunch of acid (scales with caster level, buy a higher CL wand). Fearsome Grapple is a level 2 spell, so 4500gp, i.e. 'you can afford it', and adds +4 to your grapple mod. Another level 2 is Balor Nimbus, 6d6 to anyone grappling you per round. Corrosive Grasp creates multiple touch attacks, so you do normal grapple damage and it sets off the touch attack for +1d8 acid each time. Fist of Stone gives +6 enh to strength and a natural slam attack, but only for a minute. Of course, timing all this short-duration buffing requires an ambush on your part, so why not buy a wand of Chameleon to help hide, or Invisibility for sneaking around.
You'll also have an Octopus familiar from Stormwrack, for another +3 to grappling.
Sorcerer avoids having to make use magic device checks to use the wands - if you have a friendly arcane caster willing to sneak along with you and buff you for your grappling ambush, then you can forgo this option entirely.
Option 2: Warblade
Non Tome of Battle classes count as half initiator level for determining eligibility for maneuvers. So a level in Warblade with your 11 other levels counts as a 6th level Warblade, meaning you can select 3rd level maneuvers. A 3rd level maneuver (it's a stance) is Crushing Weight of the Mountain. It gives you the Constrict ability. Other than a Soulmeld, this is one of very few ways to get Constrict in the game without changing shape. Constrict is amazing, because ANY TIME YOU ROLL A GRAPPLE CHECK, even to /enter/ a grapple, to do unarmed damage, when they try to escape, WHATEVER, you get to do Constrict damage. Yes, in addition to your unarmed strike, yes, in addition to entering the grapple damage, yes every time they try to escape. You just squeeze the life right out of them. Crusader provides a better chassis, and also has Crushing Weight of the Mountain, but warblade has access to Iron Heart Surge which is very barbarian.
Option 3: Totemist
At level 2 in Totemist from Magic of Incarnum, you grow an extra pair of arms and add your essentia x 2 + 4 to your grapple mod. At this level, with the Expanded Soulmeld Capacity (Totem) feat, that's +12 to grapple. Also grants extra natural attacks from the arm, and other stuff from other soulmelds (short-range teleport, Spell Resistance, Natural Armour, Fire Resistance, etc).
Doesn't really do much for you this level, though. A good choice to take after you've dipped the low-hanging fruits in Warblade and/or Sorcerer.
Feat: Scorpion's Grasp
From Sandstorm, this feat lets you basically have improved grab for unarmed strikes and one-handed weapon attacks. It lets you punch someone, grab them, succeed on a grapple attempt, punch them again, and still have the rest of your actions free to punch people. The best part of Improved Grab, however, which is grappling at a -20 to count as not grappled and building a big ball of weak enemies that you carry around with you and use as a melee weapon, is sadly absent.
Feat: Snatch
Requires claws or bite, MMII. Gives Improved Grab, and the ability to fling creatures 3 sizes smaller than you far, far away. Totally awesome.
Feat: Open Lesser Chakra (Arms)
Combined with a level in Totemist to get access to Kraken Mantle, binding the Mantle to your newly opened Arms slot will give you +2 to grapple per Essentia placed in (max 3, for +6 to grapple untyped).
Item: Gloves of Titan's Grip
From MiC, 3/day activate to get +8 Enhancement to Grapple for 7 rounds. Strength boosts are usually enhancement, but nothing really enhancements grapple except Grip of Iron, so this is great. Totally great. Buy it.
Item: Scorpion Claws
From Sandstorm. Exotic weapon that grants +4 to grapple checks. Well worth it, possibly even if you're not proficient.
Notes
Scaled Horror prestige class from Savage Species requires the 'Aquatic' or 'Reptilian' subtypes. You could make an argument that as a Dragon Disciple, you're kind of doing that. If so, it picks up Improved Grab at first level. Warblade -> Scaled Horror would be a great power boost.
Black Blood Cultist from Champions of Ruin is normally great for grapplers, but you're too high level and it overlaps with Dragon Disciple, also your alignment is wrong. Avoid it entirely.
Psychic Warrior is a great class for grapplers, but at this level you get too little benefit and too few power points to be of any use. The two key powers are Grip of Iron and Expansion, but they both want Augmentation to be great. There are more Wizard/Sorc spells that benefit grappling than there are powers, so even if you grabbed some Dorjes, it wouldn't be as worth it as a Sorc dip. Check the second link for more spells/powers that help out grappling.
Aberration Blood - This feat sets you up for Inhuman Reach, a natural reach increaser. It also adds +2 to grapples. At this level, it's probably sub-par.
Best Answer
So, there are a number of problems here.
1. Poor class design
First of all, your party’s choices of class are problematic: all of them are difficult-to-use classes, where a naïve approach to them, attempting to use them to create the characters they’re described as, tends to work poorly. The exception there is the bard, but even the bard, as jack of all trades, tends to benefit immensely from being very familiar with all the options that the class brings to the table, and suffers if it ignores too many of them.
Paladin and rogue are easily the worst cases for this, but warlock isn’t much better. These are just underwhelming classes.
2. Disparity in the usefulness of specialties
Secondly, your character does have sizeable disadvantages in non-combat situations. Combat is the warblade’s thing, and while his 4+Int skills, moderate Int-usage, and improved skill list doesn’t lock him into the dumb brute archetype that, say, fighters struggle to avoid, he really is out of his element when his sword cannot answer a problem. The bard, rogue, and warlock should all be able to consistently show up the warblade in these kinds of situations.
The problem here is that combat really is the biggest focus in D&D, and the system honestly doesn’t handle non-combat situations all that well. If a game doesn’t involve a lot of combat, D&D is not a great system to use for it. (This is not to say that non-combat situations, or even non-combat-focused games, are doomed to failure in D&D; it’s just that the system itself has less to offer and success or failure is much more up to the people playing than it is to the design of the system.) So being really good at combat is a really good thing to be good at in D&D. In many campaigns, being mediocre at non-combat but stellar at combat means you’re going to have most of the spotlight most of the time; this is certainly what you are describing.
3. Different fun, different expectations
Thirdly, I strongly suspect that there is an issue of “different fun” at your table. You clearly enjoy the tactical options that warblade makes available to you; you have done some research into how to have such tactical options, and you know a thing or two about the system as a whole and how to maintain those options. Your fellow players, it seems likely, are less enthused about this. While you have taken initiative to find a class that offers you such options, they’re using core classes (plus Complete Arcane, but that was an early and major book), and did not discover the problems with the classes they have chosen.
This is a problem because they probably won’t be entirely thrilled to revamp their characters to have more tactical options like you have; that kind of thing, it seems, doesn’t interest them and represents more “work” from their perspectives. What they want is to be able to choose the basic things that the book lays in front of them, claiming they work a certain way, and for that to actually be the case. I absolutely think the fault here is in the design of the classes they have chosen (and the problem would be much worse if you were, say, a druid rather than a warblade, so the “power creep” boogie man doesn’t apply here), but that’s probably small condolences to them. In short, they don’t want characters like yours—they want their characters, without yours stealing the lime light. While you, it seems likely, would be frustrated and bored with characters lacking tactical options, such as if you played one of the classes they have chosen.
The start of a solution: Communication
With the above in mind, I believe you are in a decent position to start an honest dialog about the problems with your table. The “different fun” one is the most significant, the reason why the other issues are issues, and probably the place to start. This would be a great time to ensure the assumptions you and I have made are actually accurate. There may not actually be any problem at all. The other players may not particularly care about relative combat effectiveness. Or the problem may be less thorny; they may welcome assistance in making characters similar to yours, rather than seeing that as a chore to keep up, and then you can all play together nicely.
But assuming you do have conflicting visions for how the game should go, this discussion should be about that. You should express sympathy for their position; their fun is no less valid than yours, and you have already taken significant strides (e.g. by asking this question) towards improving the situation for their benefit. But you should also be clear about your own desires, so that they can understand why you don’t want to just play a fighter (who, quite likely, would struggle as much as their characters).
This is also a good time to ask if your character is adding to, or detracting from, their experience outside of any mechanics, but in terms of personality. Since you are new to roleplaying, I want to point you to our excellent question about “my guy syndrome” as it is a common mistake among new roleplayers, and you have hinted a little bit that you may be making some of these mistakes, maybe a little. If your character is too abrasive, and is detracting from the game, it would be good and mature to take a dispassionate, even metagamey look at the character and tweak him to be less so. It’s linked in the answers to that question, but I want to point out Rich Burlew’s Making the Tough Decisions, particularly about deciding to react differently. They may apply very well to you.
In addition to those character-personality changes, mechanically what I suggest you pitch is some minor, but significant improvements to the most problematic classes your fellow players are playing. This avoids revamping the characters, this avoids ret-conning them as some similar class, and hopefully, allows them to contribute on a more even level without having to go through the chore of learning whole new things.
Paladin—easily the biggest problem. To start, I suggest making paladin spellcasting use Charisma rather than Wisdom, or else have smite evil, divine grace, etc. use Wisdom rather than Charisma. Eliminating one or the other as a necessary ability score eases a paladin’s life considerably.
I also recommend stealing Pathfinder’s version of smite evil: instead of applying to a single attack, the attack and damage bonus applies to all attacks against a chosen creature for duration of the fight (assuming that creature is Evil). The paladin also gains a bonus to AC equal to Charisma bonus against that creature for the duration. And the usage of smite evil is returned to the paladin after the target is dead (or the paladin rests, as normal for a per-day ability).
Finally, giving the paladin 4+Int skill points per level, and possibly an expanded skill list, is wise. Pointing him towards the divine feats in Complete Divine and others, the devotion feats in Complete Champion (particularly Travel Devotion if it fits his faith), and the Battle Blessing feat, also in Complete Champion, are excellent options for a paladin. These things will go a long way towards making the paladin more competent in combat and not so incompetent, at least, out of it.
If you desire greater changes, the crusader class in Tome of Battle is, of course, excellent, as is this knight-paladin homebrew.
Rogue—sneak attack needs to be easier to use. Reduce the number of creatures immune to it (e.g. Pathfinder’s implementation has only incoporeal creatures, elementals, oozes, and swarms immune to sneak attack by default, leaving constructs and most undead vulnerable).
Rogues could also use some bonus feats. Actually, I’m going to recommend just simply giving the rogue the combat styles of the ranger class. The ranger’s combat styles are the ones that rogues gravitate towards (since they output a lot of attacks, meaning lots of sneak attack), but rangers are ill-equipped to use them due to the lack of bonus damage. Instead, or even in addition maybe, Weapon Finesse as a bonus feat at 1st, and Dex-to-damage with finesse weapons soon after, as in the Pathfinder “rogue unchained,” would be a very desirable option.
Finally, recommend to the rogue the Darkstalker feat, from Lords of Madness, and then some of the options from Tome of Battle, specifically Martial Stance for island of blades and then Shadow Blade for Dex-to-damage (assuming a melee rogue). If he isn’t already, investing in Use Magic Device, wands, and wand chambers (Dungeonscape) are very good ideas.
If you’re looking for more, I’d recommend simply giving the rogue the class features of the assassin (sans sneak attack and with death attack DC based on half level) starting as a 6th-level rogue, on top of the rogue class features. A little bit of magic can go a long way for a rogue. If even more is desired, this homebrew cunning assassin could be used instead; it’s very good.
Warlock—he just needs some more invocations, and a few more skill points. I like to give one invocation every level, plus an extra one each time a new tier of invocation is gained (so starting with 2, when least are gained, and then 1 a level, 2 at 6th, 11th, and 16th, for a total of 24 invocations. And then 4+Int skill points per level. Oh, and don’t have eldritch blast’s damage progression randomly slow down after 11th, have it keep gaining 1d6 each odd level.
Bard—one of my favorites. There are plenty of options for the bard, really; I have a decent start to using the class effectively.