If you are expected to bring a character you should definitely bring that. If you're going to make a character there you should come with an idea about the following things (but remain flexible, you idea may not be exactly what you end up with).
- Character name
- Character race (Human, Dwarf, Elf, Halfling)
- Character archetype (loyal knight, scheming wizard, back-stabbing rogue, etc)
As far as rules knowledge, the Players Handbook (PHB) helps but it will speed things along greatly if you know these few simple rules.
- For most things you will attempt (including attacks) you roll a d20 (that is a twenty sided die), add a modifier, and compare it to a target number. If your total equals or exceeds the target you succeed (hit, pick the lock, whatever).
- You have abilities. Some you can use all the time, these are called
At Will. Some you can use only at intervals. These will be Encounter or Daily.
- You have hit points and healing surges. These represent how alive/tough you are. If you run out of hit points you start dying. You can use healing surges to regain your hit points in certain situations. A healing surge usually regains one quarter (1/4) of your total hitpoints, rounded down.
- We refer to dice by the number of sides they have, preceded with a d. A d4 means a four sided die. 3d6 means three six sided dice.
- When in doubt round down.
- The DM overrules the rules.
Most of all, remember you're there to have fun! The other players and DM should be willing and able to help you with the details
Start with pre-made Characters
By which I don't mean generic characters that could be in any fantasy story, but by creating a character specifically for each of your children. These characters should be based around the characters from movies and TV shows they each seem to be drawn most toward. It's not the perfect fit that character creation is, but it can let you leap over the hurdles that character creation presents to a new player and let your children get right into the game. Your child's statement about it feeling exactly like a movie is what you want to most emulate.
Use essentials classes only, specifically MBA focused ones
Essentials classes (the Knight, the Slayer, the Warpriest for example) are built around having strong class features (always on) vs. making choices between how to use encounter and daily powers to most benefit the party. They work best in Heroic Tier (levels 1-10) and are strong classes that do not require as much optimization as the AEDU classes do. more importantly they focus on what are iconic archetypes both within and without of D&D. The Knight and the Slayer for example are both actually sub-classes of the traditional fighter. The first wears heavy armor and is all about protecting his friends while the second is about dealing as much damage as possible to monsters.
Use inherent bonuses
One of the best rules options you can take advantage of is inherent bonuses. Found in Dungeon Master's Guide 2, p. 138. as well as the Dark Sun Campaign Guide Book, p. 209 (where it was expanded) inherent bonuses take the place of magic items for the purposes of system math. At set levels the characters will gain +1, +2 etc. to their to hit rolls, damage rolls, and their defense stats. Magic items are still compatible in that their properties, item attacks, and bonuses to crit damage remain, but their mathematical bonus does not stack with inherent bonuses. Whichever bonus is largest is used.
Focus on the story and the adventure, adjudicate their actions to fit
If you were playing 4e with adults I would wholly say to depend upon the use of the powers their characters have and play the system as-is. However this may be a difficult pill for your children to swallow all at once (there are plenty of adults on the internet that can't handle 4e's separation of fluff, the descriptions and lore, from crunch, the hard rules themselves). When your children's turns in combat come up or they are making decisions out of combat ask them what they want their character to do and then based on their answer formulate what their character would do mechanically and then walk them through what their character does. This way you can introduce and have them take over parts of the rules at 1 piece at a time.
Best Answer
You can do this. It's been many, many years, but I taught myself and some friends to play Basic D&D from the box back in the 80s. I didn't even find other D&D players in my area for over a year after. This isn't very different.
1) You've invested in Pathfinder... if you go play 4E, you'll find yourself investing in that, as the games aren't compatible. 4E is fun combat-wise, but considering that it's planned obsolete (the next generation game is in playtest and won't be compatible), and that it's hard to manage characters beyond a few levels without a software subscription, I'd stick to Pathfinder. (Specifically, I have a shelf full of 4E stuff which I haven't played in awhile. The family's switching over to Pathfinder for the above reasons.)
But... that doesn't mean you can't find other Pathfinder players to play with if you want someone to teach you the game. Ask around. There might be people who don't currently play Pathfinder, but have and would be willing to pull together a game to teach others.
2) I struggle with this myself. My son's 13, and we've played RPGs starting around 10 years, and a threesome has always been slightly problematic. You'll have less trouble with Pathfinder than 4E... 4E is heavily dependent on the party filling four "core" roles and having fewer than four characters is a challenge.
But this is certainly something you can do... the primary thing to keep in mind is that most published adventures are going to be oriented toward 4-6 characters, and dropping down to two characters makes things tricky. I don't advocate players running multiple characters... it interferes with roleplay (the "pretending to be your character in a story" part) and can get confusing. So you'll want to scale back the encounters (Challenge Rating) to be appropriate to the characters' level. Reducing the number and/or hit-points of monsters, or finding a weaker (but appropriate to the story) monster if you want to keep numbers up (kobolds instead of goblins, rats instead of dire rats, etc). There are charts in the rulebook that help choose CR for encounters.
When you're past the learning stage, look at multi-classing to cope with ability gaps... if you need the abilities of a fighter, wizard, cleric, and rogue, then a fighter/rogue and wizard/cleric might fit the bill. Advancement in abilities will be slow this way... a fighter/rogue with six levels will only have the abilities of a 3rd level fighter and 3rd level rogue. You may need to ramp up the XP rewards if advancement is too slow, and encounters probably need adjusted to equal the character's highest class level and not the total level. (Skimming the rules, I don't see how multi-class advancement is supposed to work. I'm assuming you can bounce back and forth leveling up in either one at each level.)
3) My recommendation is to set the Core Rulebook aside and use just the Beginner's Box until you have the basics down. The rules aren't exactly the same, but fewer options will actually make things easier to learn. That Core Rulebook is a lot to absorb.
When you've got the basics down, pull out the Core Rulebook and either start over (create new characters from scratch), or revamp your existing characters based on options that weren't available (rebuild them according to the main rules). If someone really wants to play a race or class not in the Beginner's Box, you might allow that... but I would encourage sticking to the Box and then starting over with the characters you really wanted when you shift to the Core Rulebook. Using sample characters in the Beginner's Box adventure might help with that transition... you don't feel so much like you're abandoning something you've invested in.
Overall... don't get bogged down in rules detail. If a rule is optional, skip it until you understand the rules well. If the rules start to seem too complicated, just hand-wave it and decide what happens... you can study the rules and understand the "right" way to do it later. (Hint: The "right" way is actually the way that's most fun, regardless of what the rules say.)
Remember that you're playing out a story and not just rolling dice to see how many goblin heads you smash. Have fun being the characters, ham it up a little and have a good laugh.
Edit:
Look up the Basic Paths series from Oone Games. (DriveThru RPG, Paizo.com, etc. They're downloadable PDF adventures.)
I haven't tried these, but I'm going to give the first one to my son, who really wants to run a game. The Basic Paths series is a set of adventures designed for beginning gamemasters. They're for Pathfinder, clearly delineate options for using Beginner's Box or full Core rules, and have lots of tips for the GM on how to present and run the adventure.
0one Games produces quality stuff (I've bought several of their map products) and these get good reviews. This looks like the kind of thing that would really be useful to someone learning the game without a mentor.