I can totally sympathize with you. The problem is not truly the horses, the problem is your barn trying to pass them off as schooling horses. I was at a similar barn last year. That woman would put me on horses that would spook at the slightest thing, bite, buck, and rear. It's hard to focus and fix YOU when you have to worry about what the horse might do.
At my current barn, all potential lesson horses are put through a series of tests by my trainer and they are given 3 tries to show they are suitable. If they don't pass the tests, they are sent back or resold to a suitable buyer. She absolutely WILL NOT put one of her students on a horse with the potential to cut up unless they are an advanced rider that she knows can handle it.
I think what someone else mentioned in a lease is a great idea. I leased for several months before I found my horse and it really helped a lot.