I am in agreemant with Deserthorsewoman. The braced manner of your riding has a great deal to do with the horse bracing up.
If you have taken the hrose from an abused Charro situation and got her this far, you've done well. that's a lot of work.
But the mare is still a very worried being, and the whole stopping worries her the most. it must have been something painful for her during her past training. or, she was punished if she didn't stop fast enough , or ? But, she has a lot of anxiety about it.
I also think that the saddle may very likely be causing her discomfort at the trot or canter, and the harder you ride into the cantle, the more it hurts. Its a really hard habit to break when you learn to ride with your knee braced. it's that bracing that makes you pogo up and down when she canters.
I guess I am really just repeating what others have said, but basically it's get the horse comfortable and responding to the bit at the walk before doing a trot. that could be a LOT of walking, a LOT of small circles. Then when you go to trotting, if possible, let her trot out for awhile, wihtout stopping her. I mean let her cruise around the arena until she relaxs and drops her head on her own. she might trot the first 5 minutes all bunched up and tight, but just keep her going, figure eight, circles, whatever, not too tight, not much rein contact . Just let her go. When you're pretty sure she wants to stop, then kind of tell her she can and let her ease into the stop slowly on the loosest rein you can offer, and you DON"T brace you knee. you can "quit riding" without bracing. in fact, bracing is not quiting, it's actively doing something.