My mare would be like this if I rode her wrong. If anything goes wrong, she goes faster. So, perhaps like yours, if she loses her balance or gets faster, she thinks the solution is to run faster. This is not a horse I want to teach to curl behind the bit, so I ride her pre-emptively the way I’d suggest you ride your horse now.
It is a strength thing. So ride her correctly (from your body and seat, not your hand), but do that at speeds and or figures that don’t overwhelm the postural strength she has.
On the other hand, accept too much speed (and those are different at the trot and the canter). That’s because if you go to your hand to slow here down or stop her after she has ignored your half-halt, you’ll teach her that a big pull from your hand is coming. Any horse would stay curled if they are going to meet that much hand while they were already out of balance and falling on their forehand. So you have to focus on getting the half-halt, on getting the rock back from her shoulders without worrying about the neck. That’s easier said than ridden.
I’d suggestion one exercise to add to the logic built into the “ride a square” exercise. Here, I’d start at the canter and think of the length of stride and balance (forward or back) as being on a scale of 1 to 5. A 1 is so collected that you could step down into a walk; a 5 is a brisk but rate-able hand gallop (probably with you sitting or in a very deep half-seat-- but your butt enough in the tack to be able to influence your mare with your seat).
And then you ride her in four strides at each number. Most of the time, you’ll stay between 2 and 4. Pick up a canter and get a nice 3. Ride her there for four strides. Because I like to make sure I have forward and a good, quick hind end, I’d ask for four strides at the 4 canter. When you get that, ask her to come back to a 3. Bring your shoulders back first. While you are sitting, ask with your body again in the next stride. With a bit of collection added, now you can add some hand in the third stride. Wait and enjoy what you got (or don’t enjoy what you didn’t get) for that fourth stride.
That’s the first money shot of this exercise-- asking with your body in a gait where it’s relatively easy to collect during the moment of suspension. For a made horse like yours, this is why I’d start at the canter. You can do this at the trot, too, but it’s not as easy to ride and not as easy for the horse to change so much from your body. But they should learn to do it. A horse who can lengthen and shorten by following your post will be the horse that you don’t need to hand ride.
Back to the exercise. At the end of that fourth stride, change the pace to a 3 canter. If you got a very soft, waiting and uncurled horse, ask for a 2 canter for 4 strides. If not, go back up the the 4 canter for four strides.
The other money shots to this exercise are two: First, the horse never has to hold that collection for very long, so listening to your seat is possible, physically, and the horse gets to “hear” your seat as the half-halt aid because you are changing it often and they can feel the contrast. Second, you never try for collection long enough to need to take with your hand. That’s why I said “or don’t enjoy what you didn’t get” for that last stride. No matter what you get, who cares? the canter will change in the next stride anyway. You can come back and try again in a few rounds.
I think the “ride a square turn” works for the same reason-- it gets the rider to deliver a short, and body-based half halt.
But with a horse who can curl and run, the whole point of any of these is to really set yourself up to have to pull hard in order to get your half halt; don’t let her sucker you into giving her the hand ride (including the finally set-her-on-her-ass halt). It sounds like that’s the ride she’s already had and gotten used to.
Some of getting this right will involving learning on her part (learning to hear your body-based half-halt as an aid) and lots of it will be gaining enough strength to answer that aid. The transitions within a gait are easier than between gaits (and also, I think we ride those within-gait transitions better), but all transitions help build the postural strength you need.
I think very good riders get used to riding with a bit too much pace rather than crimping up the neck in order to get canter that they do want to ride. I think this is true for good colt breakers and for auction riders. I don’t think this is most dressage ammies. But a made-but-forward horse like yours is pretty safe. Just commit to not asking for any more collection or slowness than you can get without producing the curl. But I do think it scares them a tad to be allowed to airplane around so that we can allow their neck to stretch out. I think this is the reason for riding in one of these exercises that has a lot of half-halts in it, and for the nice “candy ribbon” serpentine and the logic of teaching the horse that you will give them an attentive ride in the way that @cnm161 mentioned.
