OP, whenever somebody says something to the effect of "this horse has more potential than just a school pony", they nearly always mean that the horse is suited to competition! Riding such a horse requires knowledge, experience, timing, and CONFIDENCE.
Take my family's horses, 2 mares, like night and day. My mother's horse is a ranch bred and broke QH. Solid, quiet, sane, but still sensitive to cues, a wonderful ride and plenty of get up and go when asked for! She even challenges my mother and makes her a better rider, but they are very beginner safe challenges (the first one was turning in endless circles at a walk *I'm cracking up right now remembering* and forced my mother to figure out how to give clear direction and make her go forward. Another was trotting when asked to walk, so my mother had to learn how to relax her body to relax the horse). This horse does seem to adjust to her rider and their experience level.
My mare, on the other hand, is for experienced confident riders only. She is extremely athletic, talented, and smart, and I spent a few years going through the "valley low" doing the green+green thing and trying to figure out how to train her. They were a few years of unhappiness and even mental torture that I wouldn't wish on anyone. But it was so worth it, because now I have a horse so talented who understands me and I understand her and she trusts me because I am confident and so will go the distance for me and do what I ask of her. If she doesn't do what I ask, I know how to make her do so.
Now you put a beginner on this horse, or even someone with just the slightest confidence issue, she can feel it. She will start out ambling along, refusing to do anything faster than a western 'wog'. If the rider does happen to have the 'oomph' to make her move faster, but don't know how to handle her in other ways, she will start ducking out and bucking, maybe some rearing if they really make her mad. Then an experienced confident rider gets on, that attitude gets out FAST and she's back to being sweet, lovely, willing, forward. SUPER talented horse and a wonderful ride, but ONLY with the right rider!
Many times in this kind of situation I will encourage the owner to continue working with the horse with the help of a trainer. Usually, one can tell that the poster really loves this horse. In your case, I don't think you do, having dubbed her a "nutcase". The problem is that this is not a 'green+green' situation. You are WAY overhorsed, she just knows so much more than you. It is not too soon to sell her back to where she came or to a new home where she will be well taken care of and find yourself a horse that you will actually enjoy. It would be in her best interest too, before she has many vices that will have to be untrained, which will devalue her.
I hope I didn't sound harsh. In all honesty I think the only thing worse than green+green is being overhorsed. Then the horse has your number AND knows more than you. If you think about it, there is no way most top competition horses can be ridden by beginners. It is the horses that are 'a lot of horse' who can be the most difficult to handle, but who go the farthest with the right handler.
Definitely don't continue jumping her. Work on the flat, you don't want to create jumping vices.
"You can do something wrong for thirty years and call yourself experienced, you can do something right for a week and experience more than someone who spent thirty years doing the wrong thing." ~WhattaTroublemaker