I am NO expert, and I could very well be wrong- but I'll give it a go anyway, now that you've been warned.
The first thing that popped into my mind is that your heels could be farther down. Your feet look relatively flat in the stirrups, which I believe is causing your body to flop back and forth in the canter flat work- with your heels horizontal like that, none of your weight is in your heels, therefore your balance is shifted.
I would suggest, to keep your hands and arms steady, to do some exercises to strengthen them. Also, when riding, remember that your elbows bend, not your wrists- the wrists stay firm, keeping your hands at the pommel of the saddle.
I'm not going to critique the jumping because one, I've had only one jumping lesson in my life so it would be silly, and two, I think the reason that you can't hold a two-point and fall down early is because you lack the strength you need in your core and legs (in my lesson I had the exact same problem- couldn't hold the two-point because I didn't have the strength. :/ ), I would suggest doing some exercises to strengthen your legs and back/abs, as I believe that will benefit your riding in general, both on flat and jumping. Also, for your heels, I would suggest standing on a step with your heels off the edge to work on stretching them down. Good luck and I hope my advice is helpful for you!!