You don't need to smack you pony!
I don't want to sound mean, but maybe look at your riding before you critisize your pony. If he didnt do it with your instructor it might not be the pony. Obviously I didnt see you riding and it may be the pony, but I always go with the thinking that horses only misbehave because of something that an owner/rider is/has done. Horses are very rarely naughty/mean by nature, they are noble, trusting, forgiving animals.
Sorry if I sound mean, I just feel very strongly about this as I work with rescue horses that have been beaten because 'they were naughty' when actually the riders couldnt actually ride and the horses just couldnt take anymore/was in too much pain to carry on, so I know what horses are like after they have a few smacks.
There is a difference in a couple wacks and beating an animal. I would never do anything to harm an animal but when Copper is out of line, he knows it the instant he does it. And that is because he gets a good wack on the flank or shoulder. I understand the whole natural horsemanship and respect it... Copper's training is based off of it. That being said, the instant he tries to do something that is either a sign of disrespect, or puts me or others in harms way a smack is needed. Also we aren't talking about punching the crap out of your horse. An open handed smack just creates a good sound that snaps the horse into line. They don't like to be startled and the sound of a smack is what is takes sometimes.
Quick story time:
My friends horse is a biter... and I mean lunges at you biter. She is a sweet horse so I really believe that she thinks it is some sort of game. Anywho. He would have to walk her through two paddocks and go to the tack room for her ground work things because he ONLY believed in running her and making her work as a correction. Once that halter is on and she is being led to the round pen... its gone. She has no way of connecting Biting=work anymore because like you said Jessie; it is a VERY big rarety that a horse has a vandetta against you... She doesn't get that something wrong was done, she just thinks it is training time. But let me tell you she came at me once
and all it took was a good connecting smack and she hasn't tried it again with me, but continues to do it with others. And it is pretty irritating actually, he looks at me like I'm amazing because I got her to not lunge at me. When in reality she knows I'm not going to play that game, it is not okay. And she isn't timid or scared of me at all because of it. All it did was create a line that isn't to be crossed.
He isn't doing it with the instructer because he knows that game doesn't fly when the instructer is riding. I like the way it was said... don't get whip happy on Bee... but use your "mom" voice and a good smack will snap him back into place. It is dangerous what he is doing...he could really hurt you without the intention to. Get on him about it... every single time, but never end on that note. Maybe outside of a lesson if he is having a bad day the moment he does it good and is minding you completely jump off and be done with riding for the day. Give him lots of loves afterwards... all the rubs and grooming a horse could want! :) He'll get the picture... good rides mean LOTS of love... disrespect means the "mom" voice come out!
Hope everything works out.