This man should have his head bashed in with a baseball bat until it is a bloody pulp. Why is this even a question? There should not even be a debate about this. I can not even think of a reason where this type of behavior would be justified. Kick him in the balls until they go up into his stomach.
Unless there's some bizarre twist to this question that is being left out, I think it's obviously a no brainer that a man should face assault charges for kicking anybody in the chest anywhere, delivery room or not and ex-girlfriend or not. I can't fathom who would say "No" to this question.
The man who was kicking his ex-girlfriend should face assault charges due to the injuries that he imposed on the woman. He should also be responsible for the disruption of the hospital and security staff as they had to deal with the outburst and confusion in a medical setting. Other patients and medical staff were distracted from their jobs and he was a creating a danger for all of those involved.
Kicking a person in the chest anytime should warrant assault charges, but this situation warrants it even more. The man had no reason to attack his ex-girlfriend, especially while she was giving birth. The man could have killed her and the child if he had kicked her hard enough. Then he would be facing charges for murder.