I have a mare that FIGHTS a regular, Dr. Bristol, or french link snaffle or elevator. She will drag me around the arena with her ears pinned. Put her in a mullen mouth pelham or a ported snaffle and she halts on a dime. May want to try her in a pelham for a few shows until she realizes she can't run through the bit.
Could also try a loose ring with a hidden loop (acts as a mild elevator).
Get her teeth checked by a different vet/dentist than you normally use. I'm amazed at how bad some dentists are.
Then I would echo the suggestion to try a Happy mouth mullen mouth pelham.
And I know it is counter intuitive, but make sure you are using your seat/legs when you do downward transitions (Sit, set hands, close legs...basically asking them to bring hindquarters under themselves by half halting first, into a halt. A lot of times, if you use hands to stop and don't set up for it, you'll get the leaning on bit and opening mouth.
And I found that using a looser noseband actually helped Jet relax. He used to open his mouth and lean, and actually went in a flash to school with my old trainer, but after leaving that trainer, getting rid of the flash, and keeping noseband a little loose, he is much happier and doesn't open his mouth.
Can you post a video of what she does? Many times it is easier to offer suggestions if we can see exactly what is going on. Have you had a pro sit on her and does she do it with the pro? A good pro can often recommend the correct bit and many have a collection to try.
Your mare's adorable! I'm a sucker for a redhead girl.
I see what you mean about her tension when she comes into the show ring, but it looks for better or for worse as though you're contributing to it with a stiff arm held close to your body. You're on a very long rein with your elbows out and your wrists bent with your hands down by the pommel and not really moving except to pull back or to give well over fences. All of these breaks between your elbow and bit magnify the "loudness" of the signal needed from your hand to her mouth and contribute to what I am seeing as an imbalance in her way of going. A long rein is fine if you never need to touch the horse's mouth, but when you do, you have to use more and lift more- provoking more response. (You can see this in the second round of the modifieds, where you really lift up on the inside rein while pulling down towards your thigh with the outside rein to get a flying change. Her head goes up, her neck goes tense, her mouth goes open.) With your hand already restrictive even when you don't need it to be, she protests an additional restriction when you half-halt (because of your long rein you have to lift your hand to pull back.) She looks on her forehand in places, particularly coming into the turns where she stretches her neck down (as compared to her higher head carriage within the line) and a bit heavy on her inside shoulder (look at the turn coming out of the white picket gate diagonal.)
Whatever flatwork you are doing at home is not particularly well represented by what is going on in the ring, and I don't think your problem is the bit. She looks like she raises her head and opens her mouth to protest a restrictive hand before the fences, and spurts forward after fences in response to the soft release you're giving her- a release from pressure which encourages her to move forward. In your shoes I would shorten my reins, carry my hands forward and up off the neck with the motion of the horse's head and neck, and focus on riding positively forward with a supportive but not driving leg. This is going to feel worse before it gets better because she is not looking like an impeccably balanced horse, and when not restricted by the hand (or balancing on it) she will probably spurt forward and motorbike around the turns. This is where good balance work at trot and canter on the flat is going to help you improve her carriage. She will very likely jump like a flailing spider monkey while she adapts to carrying herself with freedom of her front end, rather than with the restriction of your hands moving against her.
She reminds me very much of a horse I rode who would open his mouth to pull out of a fundamental lack of balance and who had become accustomed to balancing off the rider's hand. I took him back to small fences and good flatwork, got him going from his back end into a light hand, and rode to every fence on a light rein contact so that he wouldn't have a huge change in contact from before, over, and after the fence- no reason to say "Whee, my mouth is free!" and scoot on the backside. Once he felt balanced and learned that he was not going to meet resistance from my hand unless he took off bolting (separate issue,) he was able to carry himself in a relaxed fashion that did not involve opening the mouth to pull.
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Does she fight contact with the bit at home on the flat? Or can you get her to accept it at the canter and encourage her to round up a little as she goes? Watching the video it's my instinct that floating the reins is part if the problem, and if you can get her more on the bit from the start things might smooth out.
I think the standing maringale could be shortened a little, too.