I ask again and it gets to where I can't ride through it anymore and have to give up. ...
I just know that she knows she can get out of it, and maybe for all we know she was even punished for it in the past,
I appreciate you've tried to rule out physical issues, but I'd keep looking there. And yes, whether intentionally, or 'punished' with a painful saddle or with fear of the feeling, she will have past feelings having a bearing still, even if not current.
Now, assuming it's 'just behavioural', yes, 'old dogs' can learn new tricks, and in this case she could UNlearn this 'trick' - it's 'just' a matter of teaching her it will never work.
Which, given her past experience, will take some... persistence for her to change her prior 'training'. If people give up because of her behaviour, EVERY SINGLE TIME
this happens it strengthens, confirms
that this behaviour does indeed work for her, so she's likely to 'try' it harder next time, if it doesn't initially work. And she will keep trying for a fair while, in all likelihood. That means if you want her to 'get over it', you need to ensure that no matter how hard she goes, it NEVER EVER works for her again.
So... I don't blame you in the least for quitting, but if you want her to learn otherwise, not giving up(or coming off!) is the biggest factor.
So... on that note, these days I'm well over bronc riding, so... I'd just accept a walk & trot personally!