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Hello. My name is***** will be happy to answer your question.I am sorry to hear about this unfortunate situation.Please note, I cannot comment on your specific situation, as this services is only limited to general information and for any legal advice / legal service you should contact your local attorney.
Unfortunately, child support and visitation are completely to separate legal issues and the court would generally not terminate parental rights / child support, unless the child is legally adopted by another adult.
So, if the visitation is an issue, then it is important to file for visitation right away and once visitation is granted, if the mother doesn't comply with the court ordered visitation, then she could be held in contempt of court and sanctioned.
I wish you the best of luck!