Legal Question in Family Law in New Mexico

It's not clear what you want. If you want him to pay child support you should get a court order to pay child support, usually part of a parenting plan, which comes in your divorce settlement if you are or were married, or as a result of a paternity action if you were not. You can't make him see her: the parenting plan would set up a visitation schedule but generally it's the other way around - men want to see their kids and go to court to enforce their right. You can terminate his parental rights if you wanted to, for example, have your new husband adopt her, but even that will not necessarily terminate his obligation to pay child support. You can enforce a child support order by contempt actions, if child support is what you want.

If you're looking for a way to make him a better dad and be concerned about his child, I'd find a better way to spend my energy.