In Texas if the non custodial parent does not want to have visitation can a judge make them have visitation.

In no state can the non custodial parent be forced to have visitation. They can only be forced to conform to a court ordered visitation. In other words, if they are allowed visitation every other Wednesday from 7-11 then they can't show up on Tuesday. But iof that don't want to visit at all, they can't be compelled to.

Of course, its rather shameful to abandon a child that way.