Sorry to hear that you are this place of fearing the very horse that you want to keep. To be honest, you might rethink the keeping her decision. I am not suggesting that a person should give up every time they start having difficulties with their horse. But the overall atmoshere between you guys feels kind of uncomfortable for you. The horse may do better in the hands of someone who is not scared of her. No insult intended to you. I am scared of some horses and would not keep them if they were given to me.
I used to ride a horse that often scared me. It was that never knowing if it was going to be a good ride or a bad one that never allowed me to settle and kept me from growing as a rider. Some folks thrive on the challenge. For me, no thank you.
Now that I am riding a different horse, I enjoy riding so much more and I have become a much more confident rider, even if I ride a more challenging horse. I just needed some experiences of success, piled one on the other, to change my overall view of myself as a horsewoman.
This would be my advcice to you; think about getting a different horse that better suits your personality. Maybe not a Thbd. Maybe a nice Cob? I hear that Irish Cobs are wonderful horses.
However, here's one bit of useful advice if you want to keep working at this;
When your mare goes to put her head down, drive her forward. Do it as briskly as you dare. You will give her a good thump with your heels and she will throw her head up and leap forward. When she does, shorten the reins and move her immediately into a working trot. When she settles and brings her head down, come to a walk and walk on. Instead of pulling against her, you drive her forward.
I would look seriously into having a saddle fitter look at your mare. A painful saddle can cause some really bad behavior. Over time, the nerves become irritated, then numb and then muscle will atrophy.
Feel free to take some photos of your mare with the saddle on her back, no pad at all. Take it when she is squared up on flat ground and in good light. Front, angled, side, rear, both sides. I would love to see it.
Don't be ashamed of having fear. Only a very few horse people don't have fear. The fearful rider who gets on is the brave one.