In my opinion, this Trainer has treated you unfairly and completely taken advantage of your inexperience.
She KNEW that you were not an experienced horse person and was not familiar with how things typically work in this sort of situation.
The horse's previous owner did not ride and was no longer interested in owning. IF the Trainer had wanted to use this horse as a lesson horse, that was the perfect opportunity to take ownership for herself.
Instead, the Trainer made an arrangement whereby the OP is 100% financially responsibly for the horse's health care (shoeing, vax, vet care) PLUS full board PLUS lessons....and the Trainer gets to use the horse absolutely free.
NOT COOL!!! (Well, GREAT deal for the Trainer - LOUSY deal for you!!!)
Yes - time to speak up.
And frankly, with the way she's behaved? You shouldn't CARE if the Trainer gets upset with you. She's pulled a fast-one on you. Shame on her!
You are liable for both the horse and rider, you are paying all the fees, and you are being seriously taken advantage of. Even if the horse was used as a lesson horse prior, when ownership changed then the trainer should have formalized an arrangement with you. Using your horse without permission or knowledge is WRONG. What happens if one of those students falls, gets hurt and their insurance company decides to hunt down the horse owner? The liability issue is huge and if you eventually decide to let others ride, you need to be sure you have insurance coverage for this. The barn/trainer insurance is not enough - it only covers their rears.
It's a lot like nuts and bolts - if the rider's nuts, the horse bolts! ~Nicholas Evans