It depends, if your ex wants, and is going to have a relationship with your child. If so, I would prob allow him in during the birth for the reason that I believe it has a bonding effect when the man actually witnesses the birth and is there when the baby takes his/her very 1st breath of air.
Regardless of your personal feelings towards him I'm sure that if he is going to have a relationship with his child you would want it to be the most positive one it can be right? As for can he take the child from you, he certainly has a right to try to gain custody in a court of law. He can go for full custody or joint custody. That said, unless he has a case that can prove you to be unfit or unstable it is highly unlikely that any judge will grant him custody. The courts will not separate mother and child just because...there would have to be some pretty serious and believable evidence brought forth in order for that to happen.
So I wouldn't get to stressed about it. TIP..it is even more unlikely for a judge to separate you from your child for even a full day if you are breast feeding *wink* it's pretty hard to cut off a baby's food supply. Just sayn....