This doesn't make sense to me. If the computer is yours (or your parents'), then it's none of the school's business whether you have admin privileges or not. Why would they be restricting your account on your own computer?
I sense a misunderstanding here. Either the school's reset and other policies apply only to their own computers and not to yours, or the computer fee is just an extra fee paid along with tuition rather than a purchase and thus it actually belongs to them.
As an IT guy, this is a pretty fun scenario. My guess is that the school has a "if you use our network, you run what we want on your computer" policy. This makes it tough to tell them to shove it, as you cant get onto the network at school if you don't play by their rules.
Personally, I would buy two external drives, one as a backup, and one as a live boot drive. Have the school image on your computer during the week, then boot to your image for the weekends and nights.