[RPG] What happens when a Vampire gets hit with the Disintegrate spell

Constitution bonuses aren't converted to Charisma.

As okeefe points out, undead in Pathfinder use Charisma to determine hit points, saves, and special abilities related to Constitution. However, that rule does not mention anything about replacing bonuses to Constitution with bonuses to Charisma. If you have a non-ability in Constitution, then you simply don't gain the effects of that bonus.

Also important to note, from the undead subtype:

Immunity to all mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms).

And from the Barbarian Rage entry:

While in rage, a barbarian gains a +4 morale bonus to her Strength and Constitution, as well as a +2 morale bonus on Will saves.

Note that undead are specifically immune to morale effects, and the Barbarian's Rage gives morale bonuses. In this case, regardless of whether or not the stat boost to Con shifts to Charisma, undead gain no benefits from raging. You may want to talk to your DM about houseruling some of this stuff if he wants your Barbarian friend to keep being effective.

To my mind, the overriding rules here are these:

Alternate Form

The creature retains the type and subtype of its original form.

Undead Type

• No Constitution score.

You cannot have an undead that has a Constitution score, so since Alternate Form has you retain your type, you cannot gain a Constitution score. I believe this is “more specific” than the general rule that you gain the target creature’s physical ability scores when using Alternate Form.

You could argue the opposite way, however, that Alternate Form is a more specific case than the general rule that undead do not have a Constitution score. But note that this results in a living (has a Constitution score) undead (retains that type), which to me is a good enough reason to side the other way.

As for using Charisma in place of Constitution, this is a common feature for undead, but not a universal one. In some places, that privilege requires a feat (e.g. Undead Meldshaping in Magic of Incarnum). Depending on your build, I might want to tax you for it; Cha-to-everything is a fairly potent strategy as it is, and undead is a desirable type anyway. Getting to use Charisma for yet more things, and avoiding the “weakness” of the undead type’s lack of Constitution, might be problematic. But if you weren’t already pursuing a Cha-to-everything build, I’d probably give it freely.