Just edited my post you may have missed it Clay, maybe this will help you out abit.
It looks like you are using your whole left side to generate power, there is a bit of a slide on the backswing and when that happens it can cause your front foot to lift up as well, when your lift foot lifts up your leg will do that. You just need to think about more of a rotation than a slide backwards and to keep that front foot planted.
A quick drill i just thought of off the top of my head to keep that leg straight is to perhaps plant a stick along the inside of your front leg so you can feel when you leg is buckling like that, just work on swings to keep it straight. I notice with that leg move as well you lose a lot of rotation. If you put your feet dead together and hit a few balls (not worrying about where it goes) you will get a feel for that rotation. A shank while doing this means you are not rotating properly, if you hit it mildly straight you are dead on.
I saw you asking about Core exercises. Look up planks and side planks on google, im sure you can find video on it. I think they are the best workout for your core and once you get them down there are different variations of them.