I am licensed for Georgia and Pennsylvania and practice family/custody law. I have an office in Lawrenceville Georgia Gwinnett County. Be careful on the site as many attorneys will not be licensed for your State.
I will try to best answer your question for you.
If mother of the child is cooperative, I recommend having her execute a hand written document authorizing you to have guardianship of your nephew, including the authority to enroll him in school, identify your particular school, and also that you have authority to obtain any and all necessary medical treatment. In the event wife chooses not to be cooperative with you, I would contact children and family services in Tennessee to advise of the situation. If you let mother know that that is your alternative if she doesn't cooperate hopefully that will encourage her do the right thing. I'm unsure from your fact pattern whether the child was resigning in either Virginia or Tennessee. The key will be to try to get child to Georgia by agreement of mother and or the guardian of father. Not sure whether guardian has been named or appointed for your brother. If so that guardian can also perhaps grant you temperate guardianship of your nephew.
Once you get the child to Georgia, I would recommend filing an emergency temporary custody action granting you primary physical custody with your nephew and supervised visitation in Georgia with mother at a time the parties may agree upon.
Hence the fastest solution for getting the child enrolled in school Georgia is his mothers cooperation executing a temporary guardianship allowing enrollment in school and medical treatment. Once that happens, I would then file for custody here in Georgia because mother can revoke the guardianship at any time.
I hope this information is helpful. If you wish to speak on the telephone that can be set up to the site as well.