My horse is young, green, and off the track. So where he has a nice trot and his left lead is progressing nicely, his right lead canter is an unbalanced mess! I laughed at Riccil0ve's comment about the motorcycle, because that's exactly what I am fighting with my horse right now!
If its a stregth problem and he just needs some work, I would get a pair of side reins. Start slowly because he might be a bit confused and work your way up. You'll find as your horse gains more muscle, he'll have some back soreness. That's because he's exercising his top line.
I also switched to a slow twist bit. My horse pulls me down so hard, and picks up speed, while leaning in to the right. This helps me get him on the bit and gain a little control. But I'd consult your trainer first!
"There is something about the outside of a horse that is good for the inside of man." ~ Sir Winston Churchill