I am the mother and custodial parent, but we share joint custody.
Never. The older the child, the more likely the court will be to listen to what they have to say. It is never, however, simply up to the child.
Contact a local family lawyer. They may be able to tell you how a particular judge considers this information.
Family Law Attorney
Children do not "chose" their visitation schedule in Texas. Under your order you and dad can agree to visitation by mutual agreement. If you can't agree, then you follow the court order. Children in their teens often want to try living with the other parent - and often it doesn't last. If your child wants to live with the other parent, it is up to that parent to file something in court to change the visitation schedule. As noted above it does not take a court order - this is your child = you and other parent can work things out.
I recommend that you consult with an attorney regarding this matter.
The other attorneys are correct that the child does not get to "choose" a visitation schedule. Once the child is 12 years old, the judge has to listen to what the child's preference is as far as which parent will get to establish primary residence. The judge MAY listen to a child under 12, but doesn't have to.
As far as your question about specific visitation schedules, the judge never HAS to listen to the child's preference, but MAY do so if he or she is so inclined (see Texas Family Code Sec. 153.009(b)). In any event, the judge is never bound to follow the child's preference.