Some Advice Please!!

A rundown of my story:

I was in a relationship with a man, we tried to have a baby and I am now pregnant. He became abusive, I left and pressed charges. Meanwhile, Ive been speaking with my other ex who I already have 2 children with. I really just want to protect myself and the new baby from the biological father. Even with the ppo and assault trial going on, he continues to make threats. I document everything, and report it everytime he violates the ppo.

My question is:

The father of my first 2 children is a wonderful man who wants to accept responsibilty for the new one. I was just told by a co worker (who has some insight into cases like this), that by signing the birth certificate and affidavit of parentage, he wouldnt be breaking any laws. That by doing so, hes not claiming to be the biological father, hes only claiming legal responsibility. Does anyone know if we would get in trouble for this? Also we've even considered getting married before the new baby arrives if that would help.

Im not sure if the biological father will even attempt to see the baby at this point. But I dont trust him with her. Im worried he will physically harm or kidnap the baby.

My lawyer told me I could probably get sole physical custody, but I would rather not invite the biological father into our lives at all.

The bio father will get visitation rights if he wants them--and will have to pay support as well. If you and the ex are married the child is presumed to be his; but the presumtion can be overcome with a paternity request, which anybody involved can request from a court.