First your title made me laugh-they all have more than 1 problem some just hide them better than others.
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With the snaffle she only chews when I ride her.
She should not have bit in otherwise, so I'm assuming that you mean when mounted -you in saddle she chews, but if you are just standing with her [you on ground] tacked up with bridle on she doesn't.
Having the teeth check was great-but just as important is bit sizing.
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Next problem. My horse can NOT keep her pace. I try and keep her in a trot in the ring, and she always stops on the turns. She's fine when I lunge her, she keeps her trot well, but when I ride her, her trot is all over the place, not to mention messy. When I ride her on the road she keeps her paces just fine, stopping when I ask her to and everything. Could this have something to do with the enclosure?
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I'm using a slow twist D ring snaffle. She's also hard to turn, especially at more than a walk. Other than that, she's okay for turning. Sometimes, she'll also be a pain in the You-know-what to stop.
I got called out on this last year-but I still absolutely believe-It's always RIDER error.
Your HORSE can stay in trot, she has proved that, she does fine when your not mounted.
Or when you ride a straight line=down the road.
The problems both with forward and slowing down, from what you have discribed occur when a rider is added to the equation.
Horses have nature balance, they then need to relearn balance when we ride, we as riders need to be the best that we can to help them establish and maintain this new balance.
When a rider falls forward/backwards/sideways... the horse needs to reshift in order to keep Us on top and them from falling down.
Or if your going down the long side using the reins for some balance, most likely to try and turn a corner a much to agressive rein aid is applied, and although you are veiwing it as incorrect, the horse is actually doing what the excessive rein aid said-Stop
You seem to be Ok @ walk, this makes sense as that is the easiest gait to maintain a steady balance in.
It would be interesting if your horse did this with every rider both good and bad.
Try this-just for fun.
Find/borrow a yoga/exercise ball a sit on it like you would if mounted-without touching the floor w/ your feet how long can you maintain your balance.