The trick, in my (often controversial) opinion, is that conventional hunt seat equitation disallows for full, healthy functionality in the hips & glutes, unless the rider happens to be well educated in sports biomechanics & conditioned therein. Now, the OP doesn’t specify if she is a hunter or not; I’m guessing she is based on the nature of the problem she’s experiencing.
Stand barefoot with your feet a little wider than hip width apart. Now, take your normal light 2-point. Pay close attention to what happens to your knees & shins. In which muscles are you feeling the most effort? Staying in 2-point, arch your back - a cue I hear a lot from hunter trainers. Notice any difference in the amount of work being handled by your quads & knees versus hamstrings & glutes? Can you open & broaden across your chest & scapula? Are you able to maintain that opening?
Now, stand back up. Take your 2-point again. This time, think of your shins moving back & your butt reaching back, as if to sit in a chair that someone is pulling out from under you. Feel any difference in the levels of activation of the quads versus the hamstrings/glutes? Any difference in the buoyancy of your
upper body over your hip flexors? Next, put your finger on your sternum. As you inhale, let your sternum activate, lifting & opening against your finger.
Which feels like a stronger position in the event of the horse’s sudden lateral movement?
Now, grab a yoga sticky mat if you have one or a rolled up towel if you don’t. You just want to be able to elevate your toes about 5". Stand barefoot with your feet a little wider than hip width apart & place your roll under the balls of your feet to raise them. Try the above again, but this time with your heels down. If you have yoga blocks, try it with the block on the low side & then the medium. Observe the changes in muscular sensation all the way up the front & back of the body when the block is on the medium side especially. (This side approximates the more exaggerated heels down I see in some riders, especially those with hypermobile ankles.) What changes occur to your overall stability?