You can try. There is really no specific 'right' to 'being there' for a pregnancy. It's too vague, anyway. Do you have the right to go to her appointments with her, to be in the delivery room with her? Not specifically, no. But I have little doubt that if you assert your rights and it is proven via DNA test that you are the father, that you'll be paying child support.
You do have rights in this matter, and I am not trying to dissuade you from asserting them. I think you should. But for the sake of the care of your child, not for the possible purpose of forcing a reconciliation with the child's mother, or attempting to drive a wedge between her and her new boyfriend.