When you first start asking the horse to canter, to the horse you are doing exactly that—asking for the canter, not a particular lead. He is going to pick up whichever lead he picked up when he started cantering/galloping at the track. It will take him some time to realize you not only want him to canter, but you want him to pick up a particular lead.
I start with whatever lead they are resistant to picking up, usually the right. I always start on a circle, in this case to the right. I post the trot and put my weight into the right stirrup without leaning. I basically step into it, but not abruptly. Once my weight is where I want it, I sit the trot and allow my right seat bone to move forward – my right hip leading. With my weight in the right stirrup, the right seat bone is already heavier than the left. When done correctly, your right leg will be ahead of your left or in other words, you outside leg will be back. Be careful not to put your outside leg too far back because this will cause you to put your weight in your outside stirrup. Opening your outside hip moves your leg back causing your weight to go into the inside stirrup. Most of the time this causes the horse to pick up the correct lead. If he does not, I quietly ask for the trot, and continue to circle until he regains his balance and composure and I ask again.
Occasionally I get a horse that is “committed” to one lead or the other. When this
happens I first confirm that it is not a lameness issue. Most of the time it’s a weakness issue instead. At the track he was probably allowed to go around on the lead he preferred most of the time, developing more strength to one side for cantering. In these cases I only ask for the lead they resist for several days to a week. I do not get upset when they pick up the wrong lead, I just ask for the trot and try again. Many times the horse is heavy on the inside shoulder so when I step into the stirrup on the inside I also lift my inside rein. I do not pull back, I lift.
It’s best to canter only a few strides and then ask for the trot before the horse loses his balance. Gradually extend the amount of time you canter as the horse develops. As an aside, the horse will usually speed up when he loses his balance. Keep this in mind when working at the canter. He probably is not trying to run off, he’s more likely trying to remain upright.
When it comes time to work on flying changes, your racehorse already knows how to
do this. It was an important part of his job. Changing the your weight to the new
stirrup is all it will take, but again, he was doing it at the gallop with the aid of momentum.
The next time a race is on television, watch how the jockeys get the new
lead. You will never see them hike their outer leg back to get it. For the record, I do not recommend working on flying changes until the horse is physically developed
enough to be off his forehand. I want my horses to have three solid, balanced gaits
before I even approach this skill.