Horses can be more one-sided than the last election! In fact, they usually are. So, one goal of every serious long term schooling program is to make each horse more symmetrical—equally pliable, equally strong in both directions. The situation you’re describing is a horse which is hollow on his left side. This is letting him overbend when tracking left and causing him to fall against your right leg and through his outside shoulder. When you say he falls in going to the right, I’m assuming he also doesn’t bend to the right very well either.
In both cases, he has to learn to respect and move away from your right leg, but let’s examine each direction one at a time.
Tracking to the left, temporarily abandon your efforts to bend him—your horse is already bent too much! Emphasize your outside turning aids to push him around the circle, and try to minimize what you’re doing with the left rein. Try especially not to pull on it, and to the extent you use it to guide your horse, use it like an opening rein away from the neck avoiding any additional backward pressure that would make him pop his shoulder more. In other words, when tracking left, concentrate on keeping him aligned.
Tracking to the right, you want him to yield in his inside poll and jaw and also to allow you to move him laterally to the outside with the push of your inside leg. Do exercises in the walk where you make a very small circle asking the horse to far overbend as though he’s looking behind your right knee. Then reduce the exaggerated positioning and expand the circle with outward leg yielding to confirm the inner bend and get him off his inside shoulder and into the outside rein.
Make sure your aids stay alive in all cases. A gripping leg won’t help you. Your calf can be quite demanding, but it has to be definite and then, as the horse responds, become instantaneously soft and rewarding. And then ready to demand again. Likewise, be sure your contact doesn’t become a crutch for your horse to lean on. He should be on contact and to the bit but not against it. He has to hold himself up!
Don’t expect that you’ll use equal amounts of strength going each direction nor that you’ll be using equal amounts of strength in each leg at the same time even going in a single direction. Remember that using less of one can equal using more of the other. For instance when he bulges out to the left, a contributing factor may be that you’re over-using your left leg.
One last thought, unless you just want your horse to go forward, try not to use both legs actively in the same instant. Don’t let one negate the other. When you push with your inside leg, let the opposite one stay on the horse to receive the energy, but in that instant let it be quiet. A beat later you may need to catch him and actively redirect with the outside leg, but don’t do everything at the same time.
Oh, and if you can find a copy of my book, I tried to unscramble this very topic in a chapter there called “About Recipes—and the Queens.” See if that helps.