Either your ex is feeling so guilty that she can't tolerate being around you and feeling that guilt, or the novelty of her new romance is wearing off and she's having uncomfortable feelings of regret when she's around you.
Either way, you behaved appropriately. I would probably stop inviting her to stay or eat with you but I understand you're just trying to ease things for the kids. Still, it could look like you're pursuing her.
My guess, given her poorly thought out answers, is that she doesn't have any idea why she's reacting the way she is, so resist the temptation to read her mind. Just keep being a great dad, keep building a great new life for yourself, and try to maintain some Buddhist compassion for your ex when you can.
