I think I picked up, though, that this is her step-daughter, and her father wants to just give her what she wants. So OP may be pretty limited in what change she can really effect here.
BUT, if a COTHer came on here and said, my trainer convinced me to get this horse, and I’ve been trying for the last 12 mos to make it work, but he’s simply never going to be good and happy in the discipline I want. Even my trainer says so. And he’s a tough ride, so I feel my confidence is getting lower every day. I really think it’s time to throw in the towel and send this horse on, but my trainer keeps insisting that riding THIS horse will make me a better rider, so suck it up. WWYD?
Setting aside the question of who’s paying the bills, would anyone here tell this person to stick with this horse?
My take: is that if parents are willing to support their kid’s involvement in horses, that should be it’s own question. They either are or they are not. But that should not be a lever to control.
What I might do: Set some baseline conditions for the parents to continue supporting the horse habit (like minimum grades at school, she can’t ever use the horse fund for other things like clothes/movies, she has to exercise the horse xx hours a week.) Set a budget of $xxx a month based on current board, routine vet costs, and lessons at whatever frequency you’re willing to fund. Giver her that budget and let her control how it is spent. Deposit that $ in a bank account that you both have control over, but she writes the checks, she’s responsible to ensure there are funds to cover her costs.
Make HER responsible to see to it that this budget covers the board and routine vet/farrier care, and whatever is left over can be spent on lessons and shows or whatever extras she wants. If she wants a new horse, well then she can sell the existing one, that goes in the bank, and that’s her budget to buy a new one.
This set up would give her more autonomy, help her realize the hard fact that this new horse may require lots of money in lessons/training, which will cut into her ability to afford showing. It would naturally encourage her to find catch rides to let her keep showing while she’s bringing along the new one.
Yes, at 15 she’s old enough for tough love, but she’s also old enough to make some decisions, and own the consequences. If the OP just makes the decisions about whether she can have the horse or not – how is that teaching her anything (other than Money is a tool to control people)?