Sometimes I look around at people riding these amazing animals and I wonder if these riders are aware of their responsibility to control straightness. Obviously, there needs to be forward motion in order to get straightness but there also needs to be a responsibility taken by the rider to be in balance and self-carriage themselves. There are many riding exercises that one can do that are outlined here and are highlighted by many a good riding instructor and horseman or woman, but the first step needs to be the responsibility of the rider to be able to balance, and not use the horse to balance, to be strong enough to stay in the centre even when thrown around, to hold their body and not fall forwards onto a horse’s from legs when he jumps and lands.
The onus is on the rider to stay straight and be strong and fit and alert to the situation – and this takes off the horse training, Working on ones own alignment, stability, flexibility and strength which is best worked on off the horse, and then brought to the horse once the level is better.
There is great article here on this whole concept by Katherine Bateson Chandler. https://dressagetoday.com/instruction/straightness-align-horse-katherine-bateson-chandler