Are maneuvers like spells and bardic music, (1) where they share the same pool of readied maneuvers, and one using a maneuver removes it from both's pools? (2) Or do they ready maneuvers completely independently? (3) Alternatively, do they ready the same maneuvers each day, but each body's maneuvers granted (for Crusaders) and maneuvers used/unused is handled individually? (4) Or do they share the same pool, and must both use the same maneuver simultaneously? (5) Last and least powerful, are they like spells, and only one body can perform a maneuver each round?
Each of these options poses its own problems and advantages. The fourth (4) is probably the easiest from a smoothness of gameplay perspective, but is potentially overpowered (hello, double White Raven Tactics, I see you trying to slip past unnoticed there). It could also lead to some serious redundancy, with same-type bonuses and effects that don't stack.
The first (1) option in some ways similar and some ways the opposite: the ability to use two different maneuvers at once is undeniably strong, but while going through their readied maneuvers twice as fast is fantastic for a crusader whose pool refreshes automatically, it's terrible for swordsages and warblades (though maybe not so much if it only takes one twin to refresh the shared pool). This may be the best option, being less powerful than (2) or (3) but more in line with the flavor of Dvati craving multiple perspectives. Further, it is probably the most interesting tactically.
(2) The second option (completely independent) seems highly unlikely both with the fluff of sharing one mind and with the precedent of shared pools for spells and bardic music. It is also the strongest mechanically, and the most cumbersome from a gameplay perspective. So at least that's easy to rule out.
(3) The third option is a lot like the second option. Not quite as much versatility -- since they share the same maneuvers each day even once they get more maneuvers known than maneuvers readied -- but they have the best of both worlds between choosing to perform the same maneuver to double up or performing different maneuvers for synergy. Refreshing their maneuvers independently wouldn't help or hurt them relative to a normal character (unlike option 1), but would slow down and confuse gameplay.
(5) I really hope my final idea doesn't turn out to be the right one, because it's the least interesting possible answer. However, it may be the only way to make ToB balanced for Dvati.
At least here we've just got three basic options. (1) Both use stances independently, using the same or different stances as the player prefers. (2) Only one twin can be in a stance at one time, like with spells. (3) Both twins are always in the same stance. (Secret fourth option, both twins must be in different stances, can be ruled out because it doesn't work at levels where only one stance is known, unless their first feat must be Martial Stance. Even then it breaks down in fringe cases.)
(1) and (3): Flavor wise, the first fits with the idea of different perspectives on the same problem, and the second with the idea of being essentially one mind. I think the former wins for flavor. Mechanically, this makes some stances far more attractive than others: stances that give typed bonuses become at least partially redundant, while the ones that don't (notably including healing stances) become twice as effective (though with healing stances this is mitigated or even necessitated by the split HP Dvati have to deal with). This is less pronounced with (1), but that also makes (1) more powerful. I honestly don't know which of the two is the better option.
For (2), I have the same objection I had to the fifth option in Maneuvers; it is wasting the potential of the race. Additionally, it doesn't make much logical sense. If a stance is based on the body, both should be able to do it; if it's based on the mind they should still at least be able to hold the same stance.