If the child is still here at that time the school starts, do we enroll him in school here?

My husband his ex-wife share custody of their 9-year old son, but the mom has primary physical custody in a different state. The court papers were filed 2 years ago. The child stays with us for the summer. We buy his flight and though we try to arrange it more than 21 days in advance, his mother usually forces us to buy last minute because she won't commit to any dates we give her in advance. It costs us more money but we have no choice because we want him here for the full summer. We always let the mother know months in advance by when we need the child to return. I'm a teacher and I know a full year in advance when I start the following school year. This year it's August 11. She just texted yesterday to say she has no money for the child's return flight. She asked if we would loan her the money. She receives $500 in child support every month. We don't have the money to loan her. His school begins August 25 for the students. If the child is still here at that time the school starts, do we enroll him in school here? Do we have to find a way to get him back? It is in the custody agreement that the mother is responsible for his return flight. Do we just keep him here until she buys a flight, even if it's already part-way through the school year? If we enroll him in school here, should we contact a lawyer, and if so, would we find one here or where he lived because it's his primary residence and because that's where the initial custody agreement was filed? Thank you in advance for all responses!