If the mother is the primary guardian, she doesn't have to answer to the father for anything. If he doesn't like the way the child is being raised, he does have the option to file a suit with the Texas OAG. There isn't any law on the books that can keep the child in Texas if Mom says she can go.
I have two cases with the OAG, though, and will promise you that custody is best kept out of their hands.
Good luck.
