I'll speak on this situation a bit since I personally know both horse and rider and used to train them.
The saddle is a little too narrow for Ariat (she can't afford a new saddle atm but will eventually). He goes better bareback. His owner is a competent rider but unfortunately where they're located there is basically no one to train with and the trainer who knows anything are REALLY expensive, like $70 a lesson.
His right hind is his weak one, working him helps make it stronger so he is more regular. Chiropractic helps him.
They are a good team and well matched for each other.
I think saddle fit is a big contributing factor because he can't lift through his trapezius muscles comfortably but other issues are rhythm control and inside leg, outside rein connection, effective half halts. Guiding the shoulders through the turns and getting enough bend through the rib cage and organizing his balance up vs flat.
Inconsistency in rhythm is a factor, he needs to be more forward and have his balance assisted with half halts. Like lengthening down the long sides, shortening down the short sides and if he runs through that walk transition 3 steps trot, 3 steps trot walk 3 steps trot and sending him into a lengthening down the long side (remember post higher and use whip as you're coming out of the saddle in the post and as your hip slides forward in canter). With getting him forward, ask as lightly as you want to ask then reinforce with the whip to get a reaction. He has to be in front of your leg first. Then can organize his balance with half halts
Remember guiding his shoulders like shoulder fore through the turns with a few leg yield steps to help with his balance. Use your leg yields from 1/4 line to the wall and wall to quarter line, step in the direction of travel, look where you want to go and inside leg when his rib cage pushes into your leg and half halt as he steps under. Tap his hind end with the whip immediately following using the inside leg. You can also open the outside rein wide to help guide his shoulders over in the turns. Also remember to post into your outside stirrup through the turns, point your belly button in the direction of travel and if you're struggling with the bend looking all the way to his tail and post into your outside stirrup. Inside leg on and off to open his rib cage and help him step over. Remember where you put your weight it where you're sending his balance.
Going left he really struggles with his right shoulder. Remember to ride your 10m circles into shoulder in but without pulling on the inside rein. Remember rotate your belly button in and use your outside knee and rein to bring his shoulders around with a supporting inside leg, if he loses bend or fall out do a 10m circle and bring him back. Inside leg, outside rein.
And don't forget the transitions you learned. Engage your shoulders, hold your core still and engage both reins, release (core, shoulders, fingers release), engage your shoulders, hold your core still, engage both reins with your fingers and release the pressure until you get a reaction. Do a few times until he's respectful.
Same horse and ride combo almost 2yrs ago