I'm not really up on the legalities of this. A lot depends on what is in that document you signed with your ex-wife. You need to have a lawyer go over that with a fine-toothed comb. If you can not afford good legal advice, check to see whether there is a hot-line staffed by attorneys or legal students that you can call for advice on that document.
Do you have a copy of his birth certificate? I don't think they can legally deny you access to him if you carry appropriate identification as to who you are, and if you are armed with the birth certificate as well. There may be things you can charge your ex-wife with, as well as the so-called boarding school, if that transpires. Somebody else's suggestion that you arrive with friends, one of whom has a video camera, is a good one I think. Especially helpful would be if one of those people were from local law enforcement, but being Utah, that's going to be tough. Not impossible though, some one else might know someone who is more sympathetic to justice than they are to their local cronies.
Also, things can get murky if she has charged or subsequently charges you with some kind of harassment or physical violence incidents. Having others along for the visit also ensures that there are witnesses so the "school" can not make something up about what actually transpired.
I would strongly urge that you PM Deborah here on the forum, as she has a fair amount of experience in what you are up against. She would be able to give far better advice than I can...