I know I'm going to get hell for this

So at the end of April I moved in with a couple of guy friends and one of them started to be more than friends but said that if I ever felt uncomfortable with it we could go back to just friends. Well a couple weeks later we conceived (complete accident) and he FREAKED the fuck out. I tried to talk him through it and let him know it wouldn't be the end of the world, but after a month and a half of "I won't be able to spend money on my truck. I'll end up killing myself. You have to adopt it out or abort." I was so pissed off I decided I needed a break and went home for a weekend to visit my parents and tell them the news. Now, they are both very strong Christians but when this situation had come up with my sister they practically disowned her. They've learned a lot since then because they just hugged me and told me we would figure it out. So I decided to move home since literally everyone I knew at home was supportive and everyone in the other area was telling me to abort. Well as soon as I told my at the time boyfriend that I was moving home, he switched gears into "I'm gonna be a great dad and do all these things!" Well I honestly just didn't buy it. I broke up with him and moved home. He met with a lawyer and started talking like he was gonna push for full custody (which would be nigh on impossible considering I'm far from unfit and Georgia tends to favor moms). Then he was talking about how ungrateful I am for his "willingness" to help. I was so freaking fed up with him. Meanwhile my ex-fiancé moves in with my best friend and her boyfriend, so I wound up having to tell HIM I'm pregnant since it would have been more awkward and rude to just let him wonder and then suddenly have quite a bump. His reaction was like completely opposite. He congratulated me, said that being a mother would suit me perfectly and that I would be great, and offered himself and his mom (who I love to death) to help watch my baby if I ever need it. A few weeks later we started hanging out more and now he's a crucial part of my life. We've both changed a lot and work so much better for each other than we did before.

All that to say, he wants to help raise my son and I wouldn't have it any other way.

Well now I'm making my birth plan. My ex/bd doesn't want to be on the birth certificate so he can pay child support without the threat of jail if he misses it. Honestly I'm happy to not have him on there since it means I choose his visitation rights and I don't really care about the money. But I kind of despise him for trying to scare me into his own ideal circumstance. I know this is the situation he wanted, but I don't think he realizes how much it favors me. Anyway; birth plan. I want my parents and my boyfriend there when I deliver. The rest of my family will probably show up to show support. But I really selfishly don't want my ex to be there. He has been known to piss me off and I don't want the added stress. Would it be okay to just send him a message when it's done and let him visit at the hospital but not during labor and delivery?