Does the Snap Kick feat work on Attacks of Opportunity (letting you make another attack)?
If yes, is the -2 to attack rolls cumulative?
Yes, it does,
and yes, it is. Actually, I am not sure it’s cumulative. In a comment, annoying imp points out the most fundamental stacking rule, which says that
In most cases, modifiers to a given check or roll stack (combine for a cumulative effect) if they come from different sources and have different types (or no type at all), but do not stack if they have the same type or come from the same source (such as the same spell cast twice in succession).
Since the source in both cases is the Snap Kick feat, it would appear that the penalties overlap, not stack. That said, I could swear that somewhere there is a rule saying that penalties often stack.
Anyway, as for applying to attacks of opportunity, that much is a definite yes. Snap Kick lets you put one more attack into any attack sequence, which is what makes it so good.