I found an English hackamore, replaced the curb chain with a strap, covered the noseband with sheepskin and tried that on Nina. That seemed to be perfectly comfortable no matter which way it moved or was tugged on, so at least I had something that I could ride in.
So I set a date and school began. I did a little lunging with her tacked up and very loose sidereins added. All was well. Then I did some lunging with only one very loose siderein, mostly to see if the hackamore had any influence when only one rein was used. This was an elastic siderein, adjusted so that it asked her to move her nose just a hair off of center, not any stress or pulling.
She went ballistic, bucked and ran and reared and tried to wipe the hackamore off with her front legs. I realized that I had never tried pulling on one rein at a time before, so after her temper tantrum was over I tried it by hand and got nearly as violent a reaction, combined with trying to get away from me.
So, not counting any damage done to her mouth, I think I had found the first place that someone had taught her to fight.
But amazingly, with a week of ground work, asking her to relax and give her head with sidereins and by hand, she figured out that it was not an attack, quit fighting and began to offer movement with ears up, waiting to be told that she was brilliant!