I moved lesson barns because of this; I don’t think it’s actually all that uncommon, either (unfortunately). I think there are a lot of barns that think “this is part of horsemanship” - getting the horse out of a muddy field. I’ve even seen this argued on this board, and I was in the minority saying I didn’t think my kids or I should have to pay to go drag a horse out of the mud and groom it.
The sad thing is that with every lesson barn in my area, there were issues – this one had more safety issues than others; but their horses were better and were cared for better, and facilities were better. Sigh. If it had been just me, not also my kids, I would probably have stayed.
So, what to actually do, if there are no other/better lesson barns?
I’d definitely mention it to the trainer - let them know about the unsafe behavior and ask for them to give specific instructions and/or accompany you. Two people could accomplish this much faster and safer than one alone - separating one horse from 20 is complicated, even if they want to come with you.
If I were your parent I’d mention to the barn that they are just waiting for a lawsuit and maybe they want to reconsider their setup.
Not sure there is any better advice.