Contact police IMMEDIATELY and report these very serious crimes. Worry about custody later.
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To do a stepparent adoption, you will need to be married to your spouse for at least six months and if the child's biological father is unwilling to consent to the adoption, then you will need to satisfy due process requirements and submit to the Court proof of abandonment, meaning that he has either 1) failed to pay child support for more than one year or 2) failed to visit the child for more than one year. If you can prove either one of those abandonment situations happened, then it is likely that the court would find that a stepparent adoption is in the child's best interests.
Adoptions are tricky. Therefore, it is likely that you will need the help of a family law attorney.
Adoption may or may not be an option later, but seems to be a slow answer to an immediate problem. If there is a danger that the cousin is or will molest your daughter, trying to solve it through an adoption is going to take months and your daughter's safety would demand that something be done immediately.
If something has already happened call the police and then file a motion in the Court that entered the custody/visitation orders. If something hasn't happened yet, file the motion asking for emergency relief to modify the visitation order to, at the very least, prohibiting contact between the cousin and your daughter.
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Contact local law enforcement. Have a meeting with them. Try to provide some objective proof of these crimes. Then, seek their assistance in gathering better proof such as recording telephone calls. Worry about the custody issue later.