Instead of just pulling on your right rein bend him a little to the right and push his hindquarters over. It will also help if you know a basic turn on the forehand.
Hope this helps !
There's actually a lot more to turning than just pulling the reins. It easier to tell beginners/novices to just pull left or right as the proper way to do it involves quite a bit of coordination.
The reins are there to turn the head (flexion). In order to turn the horse, you need both flexion and bend, which is where the legs come in. In order to make a right turn, the right leg (inside leg) becomes the pillar that the horse bends around. It's on the girth to stop the horse falling in. The left leg (outside leg) moves slightly behind the girth to push the horse around and to stop the hindquarters from moving out instead. The inside (right) rein opens to flex the head and to say "this way" and this rein should remain steady. The outside rein (left) should stay elastic.
It's hard to explain, but in order to turn properly, you must feel the connect from the inside leg to the outside rein. These are actually what turn the horse. Out of them, the rein is secondary and your inside leg is doing most of the work. It's usually easier to show this that explain it but maybe someone else here will do a better job that me!
So in reality, to turn right, you actually use your right leg and left rein more than the right rein.
Another thing to consider is whether the horse is blocked on the right. If he can turn on the left rein, but not on the right, I'd check for stiffness, pain, and tack fit. I rode a horse who had a lot more difficulty bending one direction over the other. Turns out it was arthritis in his hock which made it difficult for him to step under.
Hello Alyssa :)
If you pull, that's quite normal that he doesn't understand, to make him turn you have to open your rein without pulling :)
Try this way and tell us if it works !