Legal Question in Family Law in Texas

Unable to answer based on your limited info. Generally the US courts will not allow the child to leave the US unless both parents agree. You need to talk to a family law attorney in the county where the child resides. The judge will look at the child's best interests.

Only a judge can award custody. For that to happen there needs to be a lawsuit giving the judge jurisdiction over the child. In Texas this would usually be a divorce or a suit affecting the parent child relationship. Usually you would need to file suit in the county and state where the child resides. You need a lawyer who practices in that area.