If I am correct, they must show in a chain for showmanship, unless they show in a bridle if showing english.
I also agree that the chain is a tool and not a weapon, and the trainers approach to work with this horse is all wrong.
However, I also felt like you (OP) are really misinterpreting your horses behavior. You are giving him many human emotions that horses really don't use the same way that we do.
Its great that you guys got through to this horse, but to boil it down, this horse needs to learn to accept correction, something that I truly feel he isn't used to. It doesn't have to be harsh correction, but he does have to understand it and understand it to the point that it actually has some kind of affect.
I did work with a horse whose owners "loved him" and he was "so beautiful", and then he bucked one person off multiple times and she ended up needing surgery. He had been very skittish of people and he had gotten used to them, but they never wanted to upset him. The first week that I had that horse in training, he was a little scared of me. I did not shelter him, I did not sugar coat things, I never inflicted pain on him, but the fact that I wasn't overly concerned with hurting his feelings did make him a little headshy and resistant towards people. He was spoiled, made out to be something special, and when I got specific with him, he immediately got defensive, like your horse is doing. His owners were skeptical at first, but the horse had already been given up on by other trainers and they waited it out.
That horse came to my barn last week for horse camp, less than one year after he was here for 90 days. He was the mount for his owners children, ages 9 and 12. He remembered me and my husband and was very social and respectful with us. He is a completely different horse, likes all people, and can handle correction to the point that he can learn new things easily and willingly.
Remember, you horse will always be what you treat him as. As long as he is treated as your daughters barbie doll, he will act just as entitled as Barbie.