The key to good pivots, where the horse turns on its right hind foot, is keeping forward momentum.
It sounds as if you may not be walking a large enough circle around the horse to prevent the horse from backing up — essentially, you may be crowding your horse in the turn. As you start your turn, don't rock the horse backward, but merely walk forward while pushing your hand holding the shank under the horse's chin, over but forward to encourage the turn. Be sure to keep your body closer to the horse's neck/throatlatch rather than just walking into the horse's head. The horse's shoulders need to move with the head and neck while the left front foot crosses over the right front foot. If the horse continues to back up while pivoting, then you can lead it beside a fence or wall with your body next to the fence/wall. Then practice pivoting and letting your horse feel the fence/wall with its hips, thus letting the fence/wall encourage it forward and not backing up out of the pivot. This is only a teaching tool that is sometimes helpful early on when the horse refuses to keep the pivot a forward momentum.
Another method to help teach it to keep forward momentum is walking in a circle while making the circle smaller and smaller and increasingly moving the shoulder to get the horse's front legs to cross over properly. Then, at the conclusion of the pivot, walk forward rather than stopping. Again, this supports a forward motion, keeping this activity positive and smoother than trying to push a stalled-out horse into a pivot. Getting control of the horse's body is critical in performing a pivot where the horse maintains straight alignment from head to tail. During any of these exercises, it is important that you be happy with even 2-3, 3-4, 4-5, etc., steps of a correct pivot. Build upon this during practice to increase the number of steps a horse can pivot correctly.
If the horse fails to keep its body straight, the left front foot crossing the right front foot, not pivoting on the right hind, you should stop your horse and move forward, then start again. Do not continue to ask your horse to pivot and allow it to do it incorrectly. This is not teaching the horse how to properly pivot but reinforcing negative behavior. Take small victories, reward the horse for just a few correct steps, then try for more the next time. Sometimes it is difficult to get a horse started with correct pivots, but repetition will help teach the horse the proper form. So hang in there and keep moving forward!
