I think you should have a conversation with your trainer about what she’s trying to accomplish with telling you to put your hands low in this exaggerated position and you tell her what other problems it is creating for you. Perhaps you can come up with a different visual / different approach to get to the same thing.
One example I use a lot of this kind of communication problem is the usual “shoulders back” command that results in some riders having very stiff arms, stiff back, perhaps overly arched back. They are engaging so many muscles in their shoulders that the arm is no longer independent. You can also arrive at “shoulders back” by thinking “chest out” for some or “chest up” for others. This keeps the focus for the rider off of the shoulders so they don’t tense those muscles. Instead maybe they stretch up from the diaphragm, maybe also put their head back on right, and the result winds up being correcting a too forward or rounded posture.
If your problem is with your hands or elbows or if you are balancing on the rein or something, there could be a better way to address that than what she’s telling you now. But I think you also need to have a better idea of what she thinks the problem is and to understand how it is making you focus on negative things that make you nervous like how much you are unbalanced.
I’m not so quick to jump on the trainer as some because you say she doesn’t ride the horse like that and the horse goes well. If she was trying to pull his head down too then that might be a different story.
Prior to this trainer, essentially all the horses I rode were fairly calm, even the younger ones. Some would spook here or there or get a little forward, but nothing big.