Celebrating daughters bday party with ex husband?

Ok, stupid situation!! I should def be over this one. My ex husband invited me to my daughters 7th birthday. We get along GREAT! I am 36 weeks pregnant and have been seperated from my boyfriend for 6 months. Most of my pregnancy. Mostly because he was abusive at a point which made me leave and before that one day he loves me the next he hates me and wants me out. Really?? It's so unstable. So I moved got my own place said forget it. Well on mothers day the father of this child didn't even call to say happy mothers day, nor called to say happy bday to my daughter. Blamed me for not showing up at my house when I told him I needed to go to the hospital for contractions so he was mad didn't call! ASSHole right! So my daughters bday was day after mothers day and I went. It was a blast! Got along great! Then he starts caring bcuz we are having a baby and I told him he needed to start acting like an adult or at this point I won't have him at the delivery, and she won't get his last name. Well one day is all it took he asked my daughter how her bday was. She said fun. He asked me if I went. I said ofcourse. Ses like u don't care to b in my life anyways y shuld I sit around and besides I was going not for my ex but my daughter. He flipped out said once again I'm done and ur a scandoulois b.... I pretty much said that's fine go ahead and run again and don't expect to come back. So he can say he's done with me and get on facebook talk to woman go to strip clubs and I can't accept that he's done and go to my daughters bday? Anyone think I'm n the wrong. I'm extremly emotional and hormonal so mind screwing myself. At this point my last name is my exs name and has been for 6 years and so is ny daughters. My ex husband said he didn't mind if I gave the new baby the same last name as this father is a pos. Just really tired of games and immaturity and I think that's what it is. If he was abusive it's ok to not have him b a part of the birth right? Any suggestions on these many ?s