The parents still have residual rights to the child. While you are legally responsible for the child, mom and dad still have the rights to visitation, determining whether or not the child is adopted, choosing the child's religion and other residual rights. So you have NO right to cut this child off from mom or vice versa unless you get a court order stating so.
Parents should remember 3 things: Love your kids more than you hate your ex; when you have children the relationship with the other parent is until death; your children determine what type of nursing home you end up in.
Nothing stated by me should be taken as giving you legal advice or forming an attorney/client relationship.
Attorney-GAL in Ohio.
I've removed the knife from my back, polished it, and will one day return it -- long after you think I have forgotten.