You raise a couple of issues.
(1) Protective Order. If by "order of protection" you mean "Protective Order", she will have to articulate specific facts that give rise to a risk of immediate danger. You will have to go to court to defend yourself, but if you haven't given her any reason to be afraid, she will have a hard time prevailing.
(2) Custody of Child. You need to file for divorce and ask the court to appoint you as the conservator with the exclusive right to designate the primary residence of the child; or--even better--the sole managing conservator of the child.
You will need an attorney to help you through all this. But if you are married to the mom, you may be able to get the court to order her to pay your legal bills.
Mr. Daley gives an excellent answer. You might also consider filing the motion to modify based on her living with a sex offender.
Disclaimer: This answer is intended for educational or informational purposes only and should not be construed as legal advice or creating an attorney-client relationship. Please speak to a lawyer licensed in your state for legal advice.
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