Dual Wielding need not be game breaking if done correctly. Those who are thinking of reduced accurancy for being able to attack twice in the same time is struck in the turn-based D&D mode. Actual mechanics in a 3D realtime game should be closer to life. Behold my proposed dual wielding system! (Devs make it come true please!)----->
Requirements:
1) The guns you can use in both hands cannot have a combined STR requirement more than your current STR. Hence you got to be really strong to be dual wielding bigger guns.
In VATS:
1) You can queue attacks from either hand at any time. AP costs and accurancy remain the same for the right hand weapon. So if you queue all attacks from right hand, then there is no difference between single and duel wielding.
2) AP costs and accurancy is reduced by 20% for the left-hand weapon. Damage is reduced by 10%. That means you have more flexiabilty on how to queue your attacks. You might just be able to slip a lower AP cost attack from your left-hand into the queue. Of course, due to DT, the weaker shot may deal much lower than the main weapon. This leads to quite a few strategic choices in the gun and ammo type for your off-hand.
Out-side VATS:
1) No iron sight. Right-click fires the right weapon and left-click fires the left weapon. Damage is reduced by 10% for the left-hand weapon. This is good for certain guns that take a while to between shots.
2) If you hold down both mouse buttons to fire, you cannot move without drastically increasing your bullet spread. Additional 100% bullet spread (compared to normal) when moving. Each point of AGI and STR above the gun requirements will reduced the additional spread by 10%.
Bonus:
1) You can now use and equip shields!
2) You can hold gun for ranged attacks and a melee weapon for close range attacks without switch weapons.
3) Right combination of melee attacks (example: left-left-right) can trigger unique combo/animations.
The first part sounds spot on. Your strength requirements seem to high. A +1 or +2 to the current strength sounds better.
In vats, I would leave the AP cost alone. Weapons fire/reload at different speeds and AP reflects this. Accuracy needs to be reduced some when duel wielding pistols but not with melee weapons. I also fully disagree with reducing a guns damage just because it is in your off hand. After all, if you figure in your "to-hit" ratio into DPS, then you are reducing the damage over time for BOTH weapons.
Iron sights should be removed, replacing that button with firing the off weapon makes perfect sense. The base spread should be increased. If the movement spread is a multiplier of the base spread, then nothing more needs be changed. If the movement spread is just a number added to base spread than that number should be increased some for duel wielding guns. Reload for guns should be increased as well; maybe a x1.5 or x2. Not sure about penalties to hit while moving. If it works off the base spread number, then no adjustment would be necessary.
Your bonus #3 sounds cool but I am but sure if it fits into Fallout. Most fighting games I have played get 6 or more buttons for their combos. Only having two buttons seems kinda lame compared to that. And it adds an element of difficulty that doesn't fit the RPG half. Unless the combos could be used in vats. That would be kind of cool.