What are the legal rights of a 17-year-old mother?

The rights depend upon the state she lives in. Basically, if you aren't 18, you are a minor and still subject to the rules and direction of your parents. You may be able to get emancipation in the state you live in, but one of the key requirements is to support one's self and child. But the child is yours and you don't have to give the child up unless there is a court order.