Child Visitation

My husband and his former girlfriend were not married when their child was conceived, however my husband's name is on the birth certificate and paternity was established by the court. There was never a relationship between my husband and his son until recently. Even now there is some resistance on the child's part (he's 10 now and grew up calling her now-husband "dad", so it's to be expected). We've suggested waiving my husband's parental rights and letting them go on their way with the life the child is familiar with. She's obviously intent on receiving child support and so has not agreed to do so. If my husband is going to be held legally responsible for this child, we would like to exercise his rights as a parent and establish a firm visitation or joint custody agreement. Can this be done through the existing case involving the child support order or does he have to file a separate petition and pay separate filing fees and court costs? If a separate petition is required, what would be the appropriate petition to file?