As others have said, you've got a nice, athletic swing. I bet you have a tough time hitting a controlled cut or a fade though...
As you begin your down swing, you allow your hips to move toward the ball and your 'butt to come off of the wall.' This is likely part of your pushes and shanks. Honestly, I fight this exact issues as well. I've found its a chain reaction stemming from my takeaway and the depth of my swing arc, relative to the ball.
For me, working my hands deeper on my backswing (hands moving close to my right hip and up behind my right shoulder) helps me generated a deeper body turn and better connection between my arms and by body. Intuitively, this helps me turn onto my left heel through the ball, and keeps my butt from pulling off of the wall. It's also helped my ball striking, trajectory control and shot shaping... I'm finally able to play fades on my approach shots like I've always wanted.
Good Luck. If I have time, I'll grab some of your video and throw it into Analyzr to illustrate a few things.