Your foot is too far into your stirrup, and I'm guessing, by the two vids, they are like that often. This can cause the issues with your unstable legs, simply because you can't use your heel to anchor you down into the saddle.
Especially if you are working at jumping, your stirrup height isn't all that drastic, but you really need to work at stabilizing your legs. I know, because that is my biggest flaw when riding english!!!
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."