Well now. Thanks to all the ideas and input from all of you I have formed an opinion about what is causing this weird trot, and I have done my best to observe and "test" my theory.
As suggested. I "went back a step" in my work with her.
I put a pad on her back (I have VERY sharp butt-bones because I can't gain weight properly) and hopped on and did some "just sitting here" while she wandered around the arena. I was very pleased at how much easier I found it to "feel" her hips moving - one of us must have improved a lot
I was surprised at how quickly I thought her right hip started "dipping. It turns out the hip isn't dipping - the whole leg is collapsing.
It looks to me as if my work to reduce her big grass belly and displaced ribs is "forcing" her to use her back legs differently than she used to.
From what I see on 2 old videos I have of her, she used to subtly rotate that right hind every time it was on the ground - land, twist and lift - as well as not "tracking up" as much with the right hind. This accommodated her big belly and "VERY not straight" situation.
As she straightens, that leg is trying to carry more weight as it moves more "correctly" and it just don't have enough power.
I observed her closely when she was playing around with the boys. That leg is often at a weird angle when she moves. Looking at her from directly behind, she often places that foot closer to her center-line than she does with the other back foot.
Her hips are level - even when she does this.
This is when her leg "sinks" under her and she twists either her pelvis counter-clockwise or her leg clockwise (I can't decide which of the 2 is happening) and then she has to twist her shoulders the other way to recover - so we get the corkscrew I was feeling.
I have gone back to ambling around while I sit on her back - I just give her directions on where I want her to go.
I thought we were past this phase ...
history is repeating itself, it seems. Last time around this phase lasted just over 2 months before she showed any desire to move more and/or faster.
I guess I am back to having a racehorse Thoroughbred mare who does NOT want to go faster than an amble.
I am using this time to teach a groom to ride - he is sitting on Rocket and ambling with us.