Every horse is different, so the problem could be anything.
I bought a horse just over a year ago, and I feel your pain. For the first month, he was a gem and then went totally downhill. He shied at everything, was pigrooting, half rearing, spinning in circles, you name it. We had no connection and I was losing patience quickly. I got to the stage where I even offered him to my friend, before I turned around and said, no I'll stick with it. Today, I ride him down main roads and he doesn't bat an eyelid. I took him out without his mate not long ago, and he was a gem (quite surprisingly!)
I honestly believe he was just testing to see what he could and couldn't get away with with a new handler. He learnt soon enough when I persisted that he wasn't going to get his way and now he's an angel (most days haha)
However, it sounds like your mare has already had a few traumatic experiences, and this is bound to have been imprinted in her mind now. Unfortunately, situations like this often mean you have to go all the way back to basics (this is actually what I ended up doing with my boy) and start from the ground up.
I found groundwork amazing and far more valuable than me jumping on him nervous and not trusting him. The groundwork spent taught him who was in charge.
If you're not feeding her high sugar and energy feeds, then that shouldn't be a factor. Often behavioral issues can be caused due to pain, so it might be worth getting someone out to have a look? Is there someone other than your coach that would be willing to ride her? However, if the issue is that she is just testing her boundaries, my opinion is that you will need to be the one to push her through this.
Unfortunately, the worst case scenario is that she had been drugged when you tried her. Sadly, as disgusting as it is, some sellers are still commonly doing this. If this is the case, she probably isn't as well trained as you might have been made to believe, and I would suggest sending her to be re educated.
Hopefully you sort it out soon, best of luck!