Advice needed on etiquette and beyond - by the end of the weekend

Here's my dilemma: there is a pair of twins in Maya's class that any sane parents would have separated - they are tearing each other apart. Like their parents, the boy is pleasant and liked by all while the girl - if the looks could kill she'd spread death around. As birthday parties were being talked about, the other day, Carina came to Maya - IN MY PRESENCE - and said: "Do not come to my birthday" "How lovely" I said as Maya asked: "What?" "Do you want me to say it again?" she asked. "No, try to keep your venom inside" I said and went straight to the party store to buy invitations for Maya's party next month. As I discusses guests later with Maya, I told her to say nothing to the kids who are not coming. "Like Carina did"? "Yeah, that's mean" We agree we don't invite her(them) but Maya said: but I still want to give her a valentine (we made for all the kids). I praised her for it. Yesterday, as instructed by their parents, the twins gave invitations to all the kids - including Maya. Incapable to hold a grudge, Maya wants them invited and wants to go. So far I said: that brat is not coming in my house, and you do not go. This morning though, Darrow (the brother) came to me and gave me a big hug: "Happy Valentine's day" and lated did the same to Maya. So now I feel lousy about him. Please tell me.
One more thing: one reason we don't want them here is: at another birthday party, the mother dropped them and picked them - not on time (when we left, Darrow was crying for mommy)
I have to make a decision (RSVP or not to their invitation) by this weekend.So, let me know.