So when you’re riding across the diagonal preparing to ask for the swap, you start in neutral- hips even, equal weight in your legs, legs at the girth.
When you prepare to ask for the swap, what are the aids you’re thinking about? The way I was taught to approach the swap starts with changing the horse’s balance to the new outside hind. So, in that stride, your right leg moves slightly back of the girth, your right seatbone has a little more weight than your left. Then, when the horse has changed her balance, you change the bend: pressure with the right leg, contact with the right hand, displace the left leg behind the girth and pressure with the left leg, your left seatbone might have a little more weight than your left as a function of the way your left leg moves. Is that similar to how you’re asking?
If so, the physical skills you need are for your hips to move up and down and rock back and forth while your femur is in external rotation. I started taking notes on which muscles were involved and it’s basically every hip flexor you own with a side of your QL and adductors.
So, if you were going to try some stuff on your own for awhile before going to PT, I’d be thinking about general hip mobility: hip hikes, 90/90s progressing to lifts and then rotations, CARs, lunges with pelvic tilt forward and back, banded monster walks and clamshells, lateral step-ups in front of a mirror so you can focus on not dropping your weighted hip, and whatever Yoga for the Hips videos you find on YouTube.
Standard disclaimers: my herniated discs are not your herniated discs, my scoliosis is not your scoliosis, my injuries are not your injuries and that’s good because there should only be one of us, and I’m not a physical therapist, just the retirement plan for physical therapists. Consult your medical team before taking random advice from the internet. etc.