FWIW most of my horses were rescues or poorly trained or badly trained out of previous ignorant owners. That was history once the horse was in my hands for me to train. In fact, most horses out there that you see have not had the benefit of good handling and good training or consistent riding!
If the horse was really badly trained in an abusive manner (most training is not intentionally abusive but abusive out of ignorance or bad information) I would start back at a point before that started. IF it meant going back to long lines, ground driving and so forth, then that is where we started. If it meant re-introducing the bit through a half breed or going to bosal training.. then that is what I did. Resistance is two things.. Mental and physical. The mental aspect is followed by muscle memory.. so (for instance) avoiding the bit by raising the head and hollowing the back are the muscle memories the horse develops. YOUR job as a trainer is to come up with a way to divert that energy of resistance into something you WANT.. instead of the hollow back and lifted head. What do you want? Train that.... (it requires patience and thoughtfulness.. and you love this horse so I am sure you will gladly apply both!).
The other photos of this horse still show me a horse that is not engaging her abdominal muscles and raising the root of her neck. She also does not have the conformation to make her more than an OK low level horse over fences (a 2 foot horse is what I mean). I don't think she will point her knees down (if she does, don't jump her.. those horses are flat out dangerous over fences).
Due to her conformation I would do the following to help her:
1.) Cease using her and training her in speed events for a few months.
2.) Go back to basics and get her thinking about you up there on her back.. lots of changes in direction, lots and lots of transitions, (walk/trot only), lots of things like serpentines, spirals, figure 8ts.
3.) LOTS of trotting up hills on a loose rein with the rider in a two point.
4.) A lot of work at the walk building her suppleness and responsiveness to your smallest request on a long loose rein.. do this in an arena or enclosed space.. if she runs through the snaffle sit up straight and give her slack (she won't have anything to fight and likely will stop.. if she does not stop use only one rein and turn her).
5.) Caveletti.. build up to 8, trotting, raised to a 12 inch height.
6.) If you want to try jumping, put a cross rail at the end of the caveletti (same height and still trotting). Eventually put the cross rail a full stride AWAY from the last caveletti.. (more on this when you get to it.. jumping and training jumping is something that takes time)
This is a 5-6 days a week riding program.
These exercises will help her build the right sort of muscles and build her abdominal muscles so she can better use herself and raise the root of her neck. I would not go back to speed events or advanced reining until she does a bit of horsey "body building" with these things. When you can ask for a trot from a stand (it takes time) or a halt from a trot and the horse does it four square and balanced (does not fall on her forehand) she is ready to be brought back to speed and more advanced reining.
It will be worth it too.. I bet her times will improve too.
There is something about the outside of a horse that is good for the inside of a man. ~Winston Churchill
) Dinosaur Horse Trainer