First off, make sure you do things slow, so your horse really understands. I trained my 2 year old this year at school and at the end of 16 weeks, we were scoring 90s on our showmanship patterns - this was a huge improvement from when we started, when we started, she didn't know how to lead at all and was a run-away. In the process of teaching her this, I never used a chain, a rope, handy-stick, or whip; Just a rope halter and a lead rope.
When I taught her to turn-around/pivot, I did things one step at a time. Stand facing your horse, lift your hand up and slightly towards your horses nose - this will help your horse have forward motion, to lift his shoulders, and cross her legs over instead of behind. Your horse should cross over when you step forward, if not, simply ask your horse to move his shoulder over by tapping your hand on his shoulder, if he still doesn't respond, you may need to get more agressive. Once he takes a step forward and across, let him rest. Let him know that that was what you wanted. Keep this up and slowly start asking for more steps. Eventually, you will have a full turn around.
Hope this helps. Just remember, the rest/reward is key.