Hi Rachel, I don't know if I can help you, but I do have some ideas.
If she is incredible hacking (oh, how I envy you there!) I would examine HOW you are riding her in the ring. Are you micro-managing her when you school? Are you keeping more contact, firmer contact, or not releasing the reins as much when she obeys you? What I am trying to get across is that you, possibly unconsciously, are being more dictatorial in the ring and she is showing her disapproval (yes, that happened to me, often, until I learned to LISTEN to the horse.)
Your bit, apparently suitable for hacking, may be too strong for the fiddly work in the ring. Many horses get rather restive if a too strong bit is used too firmly in the ring. Out on the trail the horse has a lot of things to distract herself from your riding, and I suspect you are more relaxed and "forgiving" on the trail. The bay mare in my avatar photo has a VERY sensitive mouth (and nose, so bitless does not necessarily help), and I am now using my second gentlest bit on her now, but on the days that my hands are bad she quickly starts slinging her head around and gets antsy (I have Multiple Sclerosis so my hands can get unsteady without any warning.)
I noticed in your pictures that your horses are in very good weight, definitely a bit heavier than I want my horses when I want peaceful rides. Many horses who get too much grain get so they are "jumping out of their skin." This can be an individual thing, some slightly overfed horses get super calm and mellow, other slightly overfed horses can become extremely hyper. I find that, when I can no longer see traces of the first three ribs after the elbows from around 15 feet away, my rides tend to be much more exciting on certain horses. I also want to be able to feel the ribs through the fat when I press down with maybe a half pound of force.
On the trail she does not know how far you will go, and may be saving her energy for in case you want to ride for hours. In the ring there is not as much need to save energy and she may be "jumping out of her skin" because of too much grain. Is there any way, for the days that you will be working in the ring, to cut her morning grain in half? You can always feed the rest of it AFTER your work session.
Check your lower legs, mares can be more sensitive to the legs. Are your legs bouncing around? I found out, on sensitive Arabs lately, that some horses prefer that I grip with my calf only, and when I give a leg aid I give a "pulse" and do not take my calf from their sides, the release is just a return to my normal grip. This also stabilizes my seat so it does not irritate the horse's back.
I would also check saddle fit. Horse's backs can change, and a previously well fitting saddle can start hurting them. Horses find the discomfort easier to ignore out on the trail where there are distractions, but in the ring they can't ignore it and will act out. A shimmable pad can be a wonderful thing to have if you horse's back is changing shape, and it can take some experimentation to find the combination of shims that works.
Riding sensitive horses can be a pain. However when I learned how not to trigger their misbehavior I became a MUCH better rider. Truly independent hands, stable lower legs, and seat bones that stay in one place when I sit in the saddle, those are the things that give me pleasant rides in the ring when the horse really, really, really wants to be somewhere else doing what it wants to do--graze, play, groom a friend, bask in the sun and sleep.
I hope this gives you some useful ideas that work!
Does your horse does that in the same kinda places in repetition (like she got used to race in a few places with fun and now you are restricting her?). They pick up habits so fast...If I was you, I would dismount her and walk her...if you don't want to fight the "bolting" or the insane prancing...and shaking. She still is not winning, but you are safe and teaching her to stay calm by just walking her for a bit, then remount and see if she calms down.