That’s a nice mare and a nice, sympathetic ride. I do know how to ride this kind of horse, OP.
From what I see of the riding in your post: I’d have the rider ask your mare to raise her head up a bit… no ducking behind the bit because, in part, that lets the horse continue to leave her rib cage low between her shoulder blades if she already wants to go that way. My young HA needed this kind of “forward and out-to-the bit” ride at first. I think ducking behind the bit and being wiggly in the neck is an Arabian thing. And it starts to matter/needs correction when you find that you can’t get this horse to carry herself in an uphill posture because the neck moves so independently of the front part of the rib cage. I hope that makes sense.
The other things I think this kind of horse needs are two things, kind of related.
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On the “how to ride it” side: The Arabian needs to be taught to accept the feel of contact in the bridle and, as needed, your leg. So following her head wherever she chooses to put it, but not letting go (and keeping your wrists and elbows soft) in something worth cementing into your horse. With repetition and strengthening, I think these horses can push up into the bridle reliably just as well as any WB.
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On the mental side of the same issue, but broadened out to your whole ride. These over-achieving, “if she asks for some, let’s offer her a lot and make a big move” horses need to be taught to wait for directions, not guess at them. So with my wants-to-please-worries-if-he-doesn’t-know-the-right-answer HA gelding, I give him what I’d call a slow and precise ride. That is to say, I ask for his posture to be exactly what I want and I accept nothing less, and I’ll wait until we get that right or correct him as many times as necessary. Same for transitions: We do it right, or we do it again; there is no over-looking some little hop-step up into the trot that I won’t want there in the long run.
If he starts to worry or guess, I think about continuing with my precision (and this is often at slow speeds) until it’s right. I remind myself that I have a very, very long attention span and I can easily not take a break until the horse gets his head back in the game and listens to my directions rather than guessing or worrying. I don’t get mad. I don’t make big moves. I am precise and I stay there. The big deal is that nothing changes and he gets no break/walk on the buckle until the horse takes up the responsibility of listening to my aids. It’s a lot of mental pressure for these guys, even while what you’d ask them to do (say, walk without bulging one way or the other) is physically easy. The mental pressure to “stop guessing and start listening to me” is what you need; it’s the particular skill this kind of horse needs to learn because it’s not obvious to him.
If you ride this busy, clueless-but-means-well mind with the slow, methodical mentality of an old professor who can easily lecture for three hours (regardless of his students’ being bored to tears), you can increase these horses’ ability to wait for direction. Really, it’s riding a horse’s mind in the way you want it to go, just as you’d ride a horse’s body in the way you’d like that to go.
ETA: That last bit is the one idea I might add to this trainer’s way of going about things. He already has “quiet” and “tactful.” But “precision” in what you ask for and the responses you get— which means the horse has to listen and take direction-- takes it up a notch. It’s the notch these horses need and it might not be obvious to a rider who already practices “quiet” as his MO.
