Legal Question in Family Law in Kentucky

That would be pretty hard for his father to do from jail.

However, it is unclear from your question who actually has custody of your cousin. Is it his grandmother? In which case, if there is a custody order in place, it might say whether or not moving him out of state would be a violation.

I would suggest your cousin's grandmother (also your grandmother?) seek local counsel to review the custody order that is in place to determine if moving is an option, or if she would be in contempt of the court's order to do so.

Regardless, at the point he turns 18, the matter is moot anyway; he can go wherever he would like.