I think you did pretty good for your first time cantering! Seems like you really need to just focus on relaxing and breathing. You seem very tense which is what is causing you to bounce. If you just relax and think about your weight flowing down through your heels you will have an easier time sitting.
In my head while I was watching the video I was thinking relax your knees, and then a half second later your instructor said it. Good for you for your first time, it takes a few rides, but you will get it. !
You did good for the first time. The more you canter the more relaxed you'll get. It looked like the horse was limping when trotting and kind of like the leg gave out more then a true stumble but since I wasn't there it's hard to make that a sure call.
Good job! The first canter is so exciting! I still remember mine.
Like everyone else has said; relax! Try to keep your hands forward and close the horse's neck, rather than bouncing up and down with your body. Your leg, heel, and posture are very nice. Just breathe, stay calm, and you'll get the hang of it soon.