Correct me if I’m wrong, it doesn’t sound like OP is concerned about paying board but double paying the “training” part of the program. It also sounds to me that this fee is on top of the grooming, accommodation, etc and there are no questions about paying those.
Is barn policy that you must be in full training to be a client?
If not policy, what’s stopping you from simply backing out of being in the full training program, and one week out of the four you do most of the riding yourself (not always feasible, I know) or pay for extra lessons/training rides that week?
However, I can 100% see why the trainer double bills for this. At home, for a training ride, we could probably assume trainer spends about an hour of her time with the horse. Quick groom, tack up, ride, and be done. At a show… is she assisting you for more than one hour a day? Is she spending her time coordinating grooms to have your horse prepped and ring side ready? I’d assume that is the case and she then deserves to be adequately compensated. I almost started this paragraph with “to be the devils advocate…” but then thought better of it - it is absolutely not wrong for a trainer to be paid for her time.