Make sure you’re telling her what to do instead of what not to do. And don’t focus on what the horse is doing. Until you fix her, there’s almost no point in worrying whether the horse is engaged from the hind end, etc. etc. Don’t worry about getting the horse on the bit.
Give her exercises like windmill arms, alphabet feet, etc. etc.
If the horse will follow calmly behind another horse, maybe do a group lesson with a beginner and work only on the rider, around and around the ring.
If the horse needs a break, work on things that she can do without involving her seat. Two point is always a good break for a horse whose rider is a bit stiff. Can she trot in two point?
As for the trail riding, I’ve trail ridden with a lot of people over the years who are never ever going to be any good at flatwork. They don’t have what i would call an independent seat and they’re never going to be capable of a first level dressage test. Their horses are perfectly content plodding along on the trail though.
It’s hard to tell from your post whether your rider is just not very good or whether her riding is so poor its abusive. I would be careful that you’re not holding your student to a standard that she’ll never be able to meet when she’d be happy and fine aiming a bit lower.