You bring up some interesting points JPT. However, it is not quite as simple as you think. First of all, a person does indeed have a right to move in this country (unless he or she is subject to probation or parole restrictions). However, participation in extracurricular activities is a privilege and not a right. The courts, federal and state, have uniformly ruled that voluntary participation in extracurricular activities requires compliance with the rules of the organization sponsoring the activities (in this case AHSAA).
Secondly, in order to even be enrolled in a new public school, a student is required by law to live in that school district. For a student to have valid residence, he or she must either live with his parents or, if the parents are not married, with the parent who has been granted custody by the courts. Alternatively, the student can reside with a person who has been appointed his or her legal guardian by the courts. In either event, the student should have to present proper documentation before even enrolling in the new school. Even an order granting temporary custody pending a final hearing would probably have been sufficient.
I expect that the student's father will speak with an attorney, if he hasn't already done so, about filing a lawsuit over what has happened. If he finds a lawyer who will take the case (and I'm pretty sure that he will), I doubt that the case will be successful.