IMO after working with a guy who emphasizes balance is that it’s the culmination of everything else going right, not something one does exercises “for”. And, of course, it’s very strongly influenced by the rider’s balance.
The thing that I’ve found most surprising is I ride my horse (instead of the pattern/movement/exercise), and it requires that I respond to what she needs in the moment.
So, if we’re doing a diagonal, if I feel a, let’s call it a “stutter”, I try to do what she needs to feel safe/balanced instead of “finishing” the diagonal. It never occurred to me. Ever. I was taught to go from letter to letter, as instructed/planned, because that’s how a test works and you train the way you show.
This approach really requires my full attention and participation.
It’s the difference between “doing a half-halt” and … well, that autonomic rebalancing and adjustment that we just do because we feel it.
The difference between “oh, good trot, I think we can canter now” and “trot-trot-canter-canter-canter”. For me, that comma creates some weird space where balance falters and the transition fails.
I’ve had to let go of this idea of what is “supposed to happen” in response to a given aid and really feel where my horse is, where my legs, seat, and spine are …
You and your horse probably have different hooks, so the important exercise is finding them so you don’t get caught unaware.
So, I’d say start with warmup-type rides and work in movements that address bend – serpentines as well as lateral elements, listen to her body, and listen to yours.
Btw, YMMV … I was tense today and had a miserable ride. No amount of “relax stupid woman” seemed to help.