For a western pivot on the forehand I first teach the horse to move his hip away from my active rein using a snaffle bit. I start on the ground, but if your horse is accepting pressure on the bit then you can start from the saddle. Basically you will take the rein to his hip, as soon as he starts to move the hip release the pressure on the rein. From the saddle you will take the rein to your hip and shorten it as necessary to get only the hip to move. Always give the horse the chance to respond to light pressure. You may have to bring his head to the side at first, but as soon as you can, you want him to keep it no farther then 4" to the side. You practice until the horse will move the hip with light pressure, then add your leg cue. As the horse gets better his head will stay out front and you will want him to soften to the point of his shoulder.
For the western pivot on hind as for reversing directions, you need control of the shoulders both into and away from the rein. You will also work on the inside foot falling under your stirrup/foot so it is out of the way for the outside leg to come across. You can get this by asking the horse to follow the leading rein and when he does not, disengage the hip until that leg on the leading rein flies under your foot then release the rein and continue until the horse will put the foot in the correct place without going to the hip. You should practice until the horse picks up and takes the foot on the active rein and goes in that direction first.
The outside rein asks the outside shoulder to follow. This I would teach by first teaching the horse to move away from the active rein. You will be asking the horse to 'leak' out his shoulder. Pick up the rein and have the horse bend to about 4" of the straight, lift the rein, look and ride out over the opposite shoulder. When the horse takes one step release the pressure and have him follow his nose at least one step before asking again. This is a muscle building exercise so switch sides often and give him breaks. Get one step and build. When he is light on the reins you can add your leg.
My cues are: heel in front of natural straight position for the shoulder and behind the natural straight position for hip. I use the natural position for following my leg or side pass.
Now you can put both reins together and ask the horse to take both shoulders in the direction you want. Always start with the least amount of pressure on the rein and add pressure in increments and slowly. Release the pressure as soon as the horse thinks about moving in the correct direction and praise often. The horse should be getting the idea of each lesson in 15-20 minutes.
Read more: turn on the hind