At this point, your son is 16. You probably have, at best, no more than two more years of child support as most places will not terminate it until the child graduates from high school, even if he turns 18 before high school graduation. Ergo, if he is entering his junior year of high school in the fall, May or June of 2014 is probably when CS will end anyway.
To a teenager a couple of years is an eternity, but it is not to the adults and it certainly is not in the legal system. In addition to the cost, it could well take the legal system several months to get the matter heard and resolved. Unless Dad resides in the same school district and residential schooling zone, your son might have to switch high schools mid-year, if you do choose to fight this one. That's not an easy transition for most kids.
BTW, at 18, even if not yet graduated from high school, he probably gets to call the shots on where he lives and even whether he chooses to go to school at all.
One thing that you will have to think about, however, is just how difficult is your son going to be if he does not get his way. I don't recommend "caving in". Kids don't call the shots here. But, teenagers are much more adept at creating "behaviorial issues" than younger children. Are you going to be able to handle these issues, if they arise?