Easier said than done, surely, but I would just invite them both and let them sort it out. You do not need to put yourself in the middle of their drama (not that you are, but you really can't invite one and not the other). Let their differences be theirs. This happens in my family (my dad and his siblings)--everyone is always invited, and if my dad doesn't feel like being around his siblings, he doesn't go (but that's rare, and only when he won't be missed). Hopefully, they can be cordial for your daughter's sake, if for no one else's. If you send invites to each of them, however, I would maybe let them know (when you see them or are on the phone) that both are being invited so at least neither is surprised. If either of them causes a scene at the party (if they are both adult enough to put aside their differences for the afternoon and attend), you can ask them to leave at that point. So, I'd give them the benefit of the doubt (for now) and invite both--this is your daughter's day, not theirs. Sorry if this won't work for your situation, but I like to imagine that adults can behave themselves for short durations for the well-being of other members of their families...
Good luck!