Honestly? I'd probably go about looking for a new barn anyway. It would make me really uncomfortable if the barn owner was ballsy enough to use random boarded horses in lessons without monetary compensation for the owners. I also wouldn't be surprised if she used your horse without your knowledge if she was in a bind. If you really want to stay at this barn I'd tell her that YOU are the only one to ride your horse so as not to interfere with his training. If she does anything other than say "ok, that's fine!" Then I would say that you don't have to explain yourself, and that legal action will be brought upon anyone that rides her without your permission.
I had a similar issue in high school. The therapeutic riding lady asked if she could use my horse in lessons because he's fairly quiet. I said no because he's in full work and training. She then started the "oh, well it's not that much extra exertion, and they can tell the difference between the therapeutic lessons and real training so it won't interfere..." And I said "no, I just don't want him to be used." She did mention from time to time how great he would be for the program, but since I was blunt with her she did not ask again.
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