Just from what you've said here, I think I would focus on getting the mare light again...go back to the very basics. If she's so solidly resistant to backing, I wouldn't ask for it. If you're having to ask so strongly that it's creating other problems (half rearing), then she's either confused or very, very stubborn. She needs to learn that there are positives to responding appropriately.

I'd ask for her to soften her neck, then release the reins. I'd do that repeatedly until just picking up the reins would have her softening her neck immediately. Then, I'd ask for a single step back...or even just a shift in body weight back. Baby steps.

Another thought would be to get a helper. Will she back with a cue from the ground? If so, ask (lightly) for her to back from the saddle...as soon as she doesn't, have the person on the ground be the reinforcement. Not pulling more or using your legs. As soon as she backs one step, release the reins again.

The sad thing is that I think this has been "created" in her. It's going to take some serious work to fix it, but didn't you say you're not being paid to train her? And what fixes it when you're in the saddle may not fix it permanently. If her owner has hard hands, then she's going to become resistant again.

Cindy