Since very few horses, are ambidextrous, it's inevitable that the lateral dressage movements like leg yields, shoulder-in, haunches-in, renvers, and half passes will be easier in one direction than the other.
Your goal for lateral movements in dressage (and everything else you do with your dressage horse!) is to strengthen his weaker hind leg, make his stiff side more "bendable", and his hollow side less "soft".
So, for now, let's just talk about making the weak hind leg stronger. Your dressage horse's weaker hind leg is the hind leg on his soft side. There's nothing wrong with your horse! Almost every horse has a weaker hind leg because few horses are ambidextrous. The weak hind leg is the hind leg on your horse's "soft" or hollow side. His strong hind leg is on his stiff side.
The weak hind leg doesn't step directly underneath your horse’s body. Your horse displaces this leg slightly to the side to avoid carrying weight with it. On the other hand, the hind leg on the stiff side carries more weight. The issue here goes back to that old saying "use makes the muscle". If you don’t work on strengthening the weaker leg, the weak hind leg gets weaker, and the strong hind leg gets stronger.
This can lead to all kinds of problems with dressage movements down the road like having an uneven contact with the bit, uneven lengthenings, and difficulty doing lateral work in one direction.
Avoiding carrying weight with the weaker hind leg can be very subtle. Often your dressage horse will put his hind leg only an inch or so to the side. An observant ground person can tell you which hind leg your horse is "unloading". Walk and trot straight away from her. Then change direction and do the same.
If your dressage horse's left hind leg is weaker than his right hind leg, he'll carry it slightly to the left regardless of which direction you're going. Since this evasion can be subtle, your correction can be subtle as well.
The solution is to ask your horse's left hind leg to do a little "weight-lifting". Do this by moving his hindquarters an inch or so to the right so his left hind leg has to step under his body. Ask for this position in both directions on all lines and curves. This will give his weaker hind leg an opportunity to get stronger. One word of caution here. Since you know this leg is weaker, be sure you give your dressage horse lots of walk breaks so he can relax his muscles. There’s a fine line between strengthening muscles and making them sore.
If your horse is a bit more educated, you can do the same sort of exercise by always placing him in a very slight shoulder-fore or renvers position when you track to the left. When you track to the right, put him in a very slight haunches-in position. Every position should place his left hind leg a hair to the inside of his left front leg. Once again, moving the hind leg over an inch or two is more than enough to do the job.
If you do these "hind leg strengthening" exercises thoughtfully, over time your horse will be able to do the dressage movements like leg yields, shoulder-in, haunches-in, renvers, and half pass equally easily in both directions.
A Happy Horse