You need to sit down with a matrimonial lawyer. This situation raises a lot of issues, not really appropriate for a message board.
If you'd like to discuss, please feel free to call. Jeff Gold Gold, Benes, LLP 1854 Bellmore Ave Bellmore, NY 11710 Telephone -516.512.6333 Email - Jgold@goldbenes.com
There are two issues that need to be dealt with here.
First is the question of your contact with your child. As a natural parent, you have an absolute right to be a part of the child's life.
The child has an absolute right to support from you. Even if your name is not on birth certificate, she can institute an action for support at any time and once you paternity is established, you are obligated to pay support.
Whether she puts your name on the birth certificate or not is irrelevant. Your can initiate a paternity case if you want to have a role in the child's life and she can do the same to get child support. Those are absolute and you can not relinquish your parental rights and avoid child support. See a Family Law attorney to get more advice.
The above is a general answer and is not considered legal advice. You should contact an attorney before proceeding to take any legal action, signing any papers or upon service of a summons. Howard E. Knispel 631-864-7589
The fact that she does not disclose your name on the birth certificate does not negate the fact that you are the child's father, if in fact you are. If you want to be a part of the child's life, file a paternity petition establishing that you are the father and then file a petition for custody/visitation. She cannot prevent you form being in the child's life. As for a confidentiality agreement, sure the two of you can do that without a problem. However, entering into an agreement does not preclude her from filing family court petitions down the road, if she wants to do that.