I know it's scary to think about letting S17 go, but let's look at it objectively:

Do you NEED S17 to stay? That is, is he helping you with the younger kids in some way that you can't survive without? That's a lot to put on a 17 year old, but if you can't get to work without him transporting the kids from school or some such, you may have no choice but to say no.

Would he be well-supervised at his coach's home? Does the coach have a wife, will they make sure he stays out of trouble etc? It's a very big thing for teenagers to move away from their peers for the last year of high school, I can understand where he's coming from.

Does he need to escape the pain of the marriage breakdown? It's a lot for a 17 year old to handle and you might be doing him a favor by letting him get away from all the drama and pain.