Alright, time to bring out the big guns. It's possible that if you came to your parents with evidence of how harmful these institutions are--after all, it's likely they weren't provided an accurate picture by their recruiter--that they'd reconsider, but I have my doubts. Since your parents don't seem to care about your opinion on the situation, you're going to have to find someone whose opinion they do care about. It may be their religious fanaticism that got you into this mess, but maybe it can also get you out.

Are your parents active in the church? Obviously, if your parents' church is in any way affiliated with this "boarding school"--if they help fund it, get kickbacks for referrals, or even just support this sick kind of "tough love"--this may not work. But not all religious persons are as fanatical as your parents. If you think you can get support from your parents' church, go for it. Go straight to the pastor and explain the situation, bringing evidence that your parents are about to send you to an institution that condones physical and psychological abuse, ask for help, and maybe even seek refuge/support from the youth group. You may even explain that you understand you "strayed from the path of God" and want help "learning to embrace Him again," but that you want to be close to the parents you love and want the "expert" advice of the pastor and his church to help you along the way. You wanna go to their church to learn to embrace God again, not this weird camp in Mexico. Who knows what kind of doctrine they teach? It's a lie, obviously, but be fucking sincere; this is serious.

If your parents are as fanatical as you say they are and are intimately involved with the church, I have my doubts they'd risk their reputation there by sending you away to one of these horrible places against the advice of their pastor and/or the church elders, particularly if you comitt to going to youth group once a week or so.

It'll suck, but you gotta do what you gotta do to survive; good luck.