Sorry ladies but i have a different opinion. I don't know the full history between you two, but it seems to me like your not on bad terms and seem civil. It doesn't sound like he is a threat to you or the baby either. If he was or you weren't on good terms at all etc then i would completely agree that he probably shouldn't be in the room etc. But with you both being civil, i think its slightly unfair to restrict him from seeing his baby being born into the world. Especially since you mentioned this was his first child.
I have been in labour before, and know how stressful and hard it can be. I also wouldn't want someone i didn't get along with or didn't feel comfortable with in the room. So i do understand your side, i honestly do. However, if i was in your situation i would propose a compromise. I would suggest that he stays outside in the waiting room or close to the delivery room whilst your going through the phases. Then when its time to push (as long as everything goes to plan with the delivery) then the mw could call him in and he could stand at an appropriate place to witness his child entering the world.
I know this might not be what you want, and of course when it comes down to it - what you want is what will go. BUT having said that, my dad missed the birth of his second child because of traffic and he was too far away and he was completely gutted. Maybe just think of it from his perspective for a moment. Plus you don't want your LO to ask you 10 years down the line why their daddy couldn't be at the birth when you were on good terms etc.
Please don't take any of this post the wrong way btw, just some advice from the other side of the spectrum. Like i said, i don't know either of you or your situation. But you could always ask him to step outside after baby is born so you can be cleaned up and so can baby. He can go and tell his family that baby is born etc, and then come back in after you have had time to feed baby and bond a little. I'm not suggesting he be there 24/7.