The TWF fighter does less damage than a two-handed fighter on a single attack action (about 35% less), but virtually ties with a full attack action. Letting the TWF fighter always get his full attack damage significantly unbalances the equation in the other direction.
The thing is, whichever configuration you take, you can work on infinitely twinking it out. Two-weapon fighting is better when you want many more attacks. Being a rogue with sneak attack is the number one example of this. Or if you bleed per attack (like with Bloody Assault). Or use poison. Or use the various critical effects from the critical feats. Or want to use some of those attacks for trip/disarm/sunder attacks. There's a bunch of ways to increase your TWF damage by stacking "per hit" things on top.
Two-handed is better when something has DR or you're only getting one attack action in. Per-attack damage plusses and minuses and additional conditions affect a two-weapon fighter much more than a two-handed fighter - a "bard bonus" is multiplied in value by number of attacks. And as you note, you have to get a full attack to get those other attacks... But that's the same thing with a L11 two-handed fighter, they lose out on a lot of attacks when they can't stick and hit.
A straight fighter will do more dps in an abstract sense with a two-handed weapon than two-weapon fighting, if all he does is straightforward hitting without any other interesting feats. But if you change the TWF rules, your player is just going to turn around and layer the other TWF twinks on top and suddenly it's the more powerful thing, and you have to start worrying about your two-hander player... Because he who inflicts the most damage wins the game, apparently.
Also, there's a difference between optimization and real play. Real adventurers find gear, they don't "have 32000 to spend on it." I've played and GMed a lot of Pathfinder, and players have run and enjoyed two-weapon characters as much as two-hander characters. (Sword and board, however, sucks.)
Since the peanut gallery demands "math," here's some reasonably maxed out L11 characters, using all the Paizoey goodness. Each has more special abilites than one can reasonably enumerate, but I tried to stick to "jack up the numbers" options as much as possible. Full builds are below, but the relevant stuff here is that:
- 2HGuy, attack action: +23 (4d6+29/19-20 plus 1d6 fire plus 1d6 cold) 19-20 x2 - power attack, overhand chop is giving double STR to damage, vital strike, furious focus
- 2HGuy full attack: +23/+15/+10 (2d6+25/19-20 plus 1d6 fire plus 1d6 cold, 2d6+29 for attacks 2 and 3 from backswing) 19-20 x2
- 2WFGuy, attack action: +15 (1d6+15/17-20 plus 1d6 fire)/+15 (1d6+12/17-20 plus 1d6 cold) 17-20 x2 - two attacks from Doublestrike, piranha strike is like Power Attack for Dex, if he hits with both then 1d10+1 rend, if he crits +2d6 bleed, agile weapon enhancement gives +dex to damage
- 2WFGuy, full attack: +17/+12/+7 (1d6+17/17-20 plus 1d6 fire)/+17/+12/+7 (1d6+14/17-20 plus 1d6 cold) 17-20 x2, if he hits with both then 1d10+(1.5x Strength modifier) rend, if he crits +2d6 bleed, agile weapon enhancement gives +dex to damage, +2/+2 during full attack from twin blades, and also +4 AC bonus from two-weapon defense and defensive flurry)
Versus let's say AC 25, the average DPS (including crits and rend) for each is:
- 2HGuy, attack action: 55.67 (plus maybe shaken)
- 2HGuy, full attack: 87.06 (plus almost guaranteed shaken)
- 2WFGuy, attack action: 35.55 (plus two points of bleed)
- 2WFGuy, full attack: 81.80 (plus 5 points of bleed ongoing)
So yes obviously, in high mobility situations the 2WF guy loses out (though he does get two attacks, not one, from his archetype), but he's pretty much neck and neck in a full attack situation, any slight change to any of these numbers makes the winner of the full attack follies go back and forth. Both these characters have loads of other fun stuff to do, they have more feats than they know what to do with. The TWF guys is obviously much tighter on feats and stuff. Keep in mind this is a straight fighter compare, and there's other ways to fill out TWF and all those rogues with sneak attack can stack a lot of damage on... Go look at some build guides and there's plenty of L11 twf builds out there that do a lot more than this.
Does the TWF guy lose? Yes. But the question is, "is the answer to let him have his 81-point full attack with a standard action?" The answer to that is no, it unbalances it back the other way.
Full builds
Because everyone has stat boost items I usually don't add them, but in this case I decided to make up the wealth differential caused by the weapons with a +4 belt of strength.
2HGuy
Human (Kellid) Fighter (Two-Handed Fighter) 11 (Pathfinder RPG Advanced Player's Guide 0)
N Medium humanoid (human)
Init +1; Senses Perception -1
Defense
AC 11, touch 11, flat-footed 10 (+1 Dex)
hp 114 (11d10+44)
Fort +10, Ref +4, Will +2
Offense
Speed 30 ft.
Melee +2 cruel flaming frost greatsword +20/+15/+10 (2d6+25/19-20 plus 1d6 fire plus 1d6 cold)
Special Attacks backswing, overhand chop, piledriver, shattering strike, weapon trainings (heavy blades +2, pole arms +1)
Statistics
Str 24, Dex 13, Con 16, Int 9, Wis 9, Cha 9
Base Atk +11; CMB +15 (+19 bull rush, +18 sunder); CMD 29 (31 vs. bull rush, 32 vs. sunder)
Feats Bull Rush StrikeAPG, Cornugon Smash, Dazing AssaultAPG, Dreadful CarnageAPG, Furious FocusAPG, Greater Bull Rush, Horn of the Criosphinx, Improved Bull Rush, Power Attack, Pushing AssaultAPG, Vital Strike, Weapon Focus (greatsword), Weapon Specialization (greatsword)
Skills Acrobatics +12, Intimidate +13
Languages Common, Hallit
Other Gear +2 cruel flaming frost greatsword, belt of giant strength +4, 150 gp
Special Abilities
Backswing (Ex) Attacks after the first in a full attack receive 2x STR bonus.
Bull Rush Strike Critical hit's confirmation roll is a Bull Rush maneuver check.
Cornugon Smash When you damage an opponent with a Power Attack, you may make an immediate Intimidate check as a free action to attempt to demoralize your opponent.
Dazing Assault (DC 21) -5 to all attacks and maneuvers but struck foes are dazed 1 rd (Fort neg).
Dreadful Carnage If you reduce an enemy to 0 or fewer HP, you can make an intimidate check to demoralize all enemies within 30' as a free action.
Furious Focus If you are wielding a weapon in two hands, ignore the penalty for your first attack of each turn.
Greater Bull Rush When bull rushing, foe's movement provokes AoO from your allies.
Horn of the Criosphinx Add 2x your Str bonus to damage rolls on charges while wielding a two handed weapon.
Improved Bull Rush You don't provoke attacks of opportunity when bull rushing.
Overhand Chop (Ex) Single attacks with two-handed weapons receive double STR bonus.
Piledriver (Ex) Standard action: attack with a two handed weapon, if successful, free bull rush or trip w/o AoO.
Power Attack -3/+6 You can subtract from your attack roll to add to your damage.
Pushing Assault If you are wielding a weapon in two hands, push the target 5' back instead of dealing power attack damage.
Shattering Strike +3 (Ex) +3 Sunder and damage vs. objects.
Vital Strike Standard action: x2 weapon damage dice.
Weapon Training (Blades, Heavy) +2 (Ex) +2 Attack, Damage, CMB, CMD with Heavy Blades
Weapon Training (Pole Arms) +1 (Ex) +1 Attack, Damage, CMB, CMD with Pole Arms
2WFGuy
Human (Kellid) Fighter (Two-Weapon Fighter) 11 (Pathfinder RPG Advanced Player's Guide 0)
N Medium humanoid (human)
Init +5; Senses Perception -1
Defense
AC 16, touch 15, flat-footed 11 (+1 shield, +5 Dex)
hp 114 (11d10+44)
Fort +10, Ref +8, Will +2 (+3 vs. fear)
Defensive Abilities bravery +3, defensive flurry
Offense
Speed 30 ft.
Melee +2 agile flaming cold iron shortsword +15/+10/+5 (1d6+15/17-20 plus 1d6 fire) and
+2 agile frost mithral shortsword +15/+10/+5 (1d6+12/17-20 plus 1d6 cold)
Special Attacks doublestrike, improved balance, twin blades
Statistics
Str 13, Dex 20, Con 16, Int 9, Wis 9, Cha 9
Base Atk +11; CMB +9; CMD 27
Feats Bleeding Critical, Critical Focus, Double Slice, Greater Two-Weapon Fighting, Improved Critical (shortsword), Improved Two-Weapon Fighting, Piranha Strike, Two-Weapon Defense, Two-Weapon Fighting, Two-Weapon Rend, Weapon Finesse, Weapon Focus (shortsword), Weapon Specialization (shortsword)
Skills Acrobatics +16, Intimidate +13
Languages Common, Hallit
Other Gear +2 agile flaming cold iron shortsword, +2 agile frost mithral shortsword, 150 gp
Special Abilities
Bleeding Critical Critical Hits deal 2d6 bleed damage.
Bravery +3 (Ex) +3 to Will save vs. Fear
Critical Focus +4 to confirm critical hits.
Defensive Flurry +3 (Ex) +3 AC vs. melee when making a full-attack with both weapons.
Doublestrike (Ex) Standard action: Attack once with each weapon (normal two-weapon penalties).
Improved Balance -1 (Ex) Reduce the penalties for two-weapon fighting or count off-handed one-handed weapon as light.
Piranha Strike -3/+6 You can subtract from your attack roll to add to your damage with light weapons.
Twin Blades +2 (Ex) +2 to hit and damage when making a full attack with both weapons.
Two-Weapon Defense +1 to AC while wielding 2 weapons. +2 when doing so defensively.
Two-Weapon Rend Deal extra 1d10+(1.5x strength modifier) if you hit a foe with both main and off hand weapons.
No, a PC cannot make use of the devil's poison
The hellish weapon is a special trait of the creature, not of the weapon. Therefore, the trait only applies when the erinyes is wielding the weapon.
In addition, the trait specifies that "The erinyes’s weapon attacks are magical…" not that the erinyes's weapons are magical. The devil could just as easily hit a PC with a chair, and the improvised weapon would still deal poison damage.
Best Answer
By discussing it with their players
If the players refuse because they want to keep their overpowered weapons, tell them you're not enjoying the game and tell them to find somebody else to DM for them and simply start a new game with all the experience you've learned from your previous campaign.
Nobody's first time DMing is the best time ever, but don't feel trapped in a campaign because a bunch of spoiled players refuse to give up their toys.
New DMs most likely don't have the knowledge to make balanced homebrew weapons
Several of these homebrew items are absurd at all levels. Take, for instance, the Bogsword. An extra 2d8 damage is already insane, but it has a component that stacks with itself for insane amounts of damage per turn.
A level 5 fighter with this weapon can attack twice, then action surge to do it again and, depending on what kind of weapon it is, might be able to attack an additional time with a bonus action. Even if we assume they don't get a bonus action, this means that the first round, they've stacked 4d6 acid damage on the enemy.
The next round, they attack twice. The creature has taken 4d6 acid damage already, and now they've been stacked up to 6d6 acid damage. I don't even know how you're ruling the duration in terms of stacking, but at the very least they can take 8d6 acid damage in a round before their duration runs out. This is insane for a bonus effect ontop of an item that already does more damage than what can reasonably be expected from a Very Rare of even Legendary item, because nothing is going to resist that 2d8 magical slashing damage either.
Balance within the party is messed up
I see quite a few suggestions that suggest simply increasing the HP of the enemies the DM is throwing at the players. That works to fix the problem of enemies dying before they even get a single round, but that'll only make the fact that these items are not evenly balanced all the more obvious.
The Barbarian is rocking reasonably balanced items, albeit balanced for a higher level than he currently is. Contrast this with the Bogsword and the Rocket Launcher and simply raising the HP of all the enemies will make it so the Barbarian can't contribute nearly as well as the Fighter or the Artificer.
My suggestion
These players are level 6. Do away with the all the homebrew items and let all the players pick a single Rare quality magic weapon. This is already a lot stronger than what you can usually expect to be wielding at level 6 in most campaigns, having a +2 weapon for example at this level is absurdly powerful, but at least it won't completely break the game like these homebrew items. Realistically, they'd be rocking a +1 weapon at this point, if they're lucky.