If you can find a trainer with a strong French Classical foundation, I think that would be best. Sounds like she would benefit from the French "balance before motion" approach vs the more German "balance through motion". It can be harder to find good ones, though. There seems to be more hacks attracted to that school...
You could even look into in-hand dressage. It wouldn't help the confidence away from you, but it can help with mentally working through difficult asks and building more balance in a low activity way. I like this book.
You might also want to try a different approach to her warm ups, depending what she's capable of. If she's turned out during the day, you could try doing a single loose rein walk then a long rein canter in a light seat. If she'd be willing and safe, of course.
Did the vets ever look for cervical arthritis or kissing spine? Pssm2? Easy to overlook, the tension when asked to do anything more can be from that. All common in warmbloods. Or it can just be a mental block.
Like the other poster said, you want to be doing in hand work in a bridle.
I do it a bit different. Reins over the head, same as them, but the off side rein comes over and your off hand holds it at the shoulder. (There's no way I could reach over the wither, my horse is 17.2!). Your other hand is holding the bit directly. Whip goes in the off side hand.
Start with basic bending and walk/halt transitions to get both of you familiar with the position. If you need to use the outside rein, you pull down against the neck. The hand on the shoulder controls where the shoulder is. If they are falling in, you give little pushes to get them to move over. If they are falling out, you take the hand off the shoulder and invite them back over. Whip can raise or lower to target the hind legs(via the barrel/hip) or the girth as needed.
When I do my leg yields in-hand, I have the whip more horizontal, resting across their side. I ask for a slight inside bend, then use my body to walk diagonally in front of the shoulder. It's very easy to lose the shoulder, so go slow, a few steps over then straighten for a few, then over, rinse and repeat. If you are losing the shoulder, straighten the neck out, go forward, and ask more with the whip for the hind leg to step under.
Doing in-hand work will really develop your feel for when they are crooked and on one shoulder more than the other, or if they've lost their balance and are diving down. If they get heavy in the hand, you lift up, ask that head to come up and shift back. There's a whole bunch of building blocks to teach them to balance themselves starting in the halt and doing flexion exercises. You stand in front of them and take the bit in both hands, ask them to balance by using the bit up and back. Then flex to the side ~45 degrees without losing balance. Then you do the same from the side, same position as when doing walking exercises. Flex them away, maintaining the balance. Eventually they can extend the neck at the end of these flexions, but it's easy to lose balance in that extension.
Other basic exercises include '4 circles' where you walk with them on a figure 8 of 10-15m circles. Ask for inside bend for one circle, then outside bend, then keep the outside, then inside. This way you work in both directions, both bends, including true bend and counter bend for each side. You should do it from both sides yourself. Another one is the Flechi Droit, you have them walking straight with the neck flexed to the inside. It takes a lot of balance for them to do this. The greater the flexion, the harder it is.
It's not super easy to find good resources to learn this online. Phillip Karl teaches this stuff, but a lot of the content isn't public. It's going to be trainers who subscribe to more French/Spanish styles of dressage that will teach in-hand work. I have this book Horse-Training-Hand-Modern-Working which is good. In that book, the "short reins" section is what you'd want.