Legal Question in Family Law in Texas

Well, he can try. What you are talking about is referred to as a modification. If he files a petition seeking modification of your prior order to get "full custody" of the kids, what he is seeking to modify is the rights you currently have to decide where the children live and to receive child support. He may also want to modify some of the other rights in your order but when folks say "full custody" these are the two rights they are usually talking about. The Texas Family Code doesn't have anything in it that says "full custody".

In order to modify a prior order, Dad must show that there has been a material and substantial change in circumstances with regard to a person affected by the order (you, him or the kids) and that the modification sought would be in the best interest of the children. If he can't show there has been a change in circumstances (except he's further behind in child support) then the threshold requirement would not be met and no modification should be granted.

As with most things in family law, the determination of what is "material and substantial change" and "best interest" is in the eye of the trial judge. If Dad actually files something you need to talk to a family law attorney who practices in the county where the suit is brought right away.