Don't squeeze your legs to get him going, all you have to do it tap lightly. Horses do feel the smallest of pressure even if they don't act like it. If you tap both legs lightly and there isn't any response, then kick him alot harder to let him know that he should be paying attention. It doesn't hurt them, just corrects them.
All horses are asymmetric like we are, so if he is more rigid it may also be a good idea to do a lot of shoulder-ins, half passes at walk to get him a bit more supple.
He is quite receptive but on his right is less sensitive..
Fist of all, use them less. Chances are if you are constantly kicking your horse to go he will ignore it. You can use light but clear pressure with your leg and if he doesn't respond you apply a crescendo with your whip where your leg is, not on the shoulder or on his hind. A crescendo with about three seconds in between each touch, starting from very light and increasing. As soon as he gives any response along the lines of what you want, even if he just shifts his weight, you stop. Then you repeat.
The horse will learn when you stop applying pressure.