I don't have as much experience as these others with stallions, but I have learned that if ANY horse doesn't behave at hime, it is pretty likely that taking him to a show will only make things worse. So I try to simulate horse shows at home as much as possible.
What I do with our basically well-behaved young stallion, is first of all have a special place, halter, and routine for breeding. Last year during breeding season, on the days he wasn't breeding, I would take him to ANOTHER place, in his show halter halter and practice for shows. I would have someone else set up and lead the mare in heat (not real close, but as might be encountered in the ring) and he was to ignore her. He may be young and hormonal, but he seemed to get the message.