I just want to preface this by saying I'm not an expert but I want to try to help.

It appears to me as though your grip runs through the middle of the palm/life line of your hands. You want to get the club running through where your fingers and palms reach to the first knuckle of your pointing finger. See this photo: http://f.tqn.com/y/golf/1/S/D/d/1/lead-hand-grip.jpg and this video at about 3:30: https://www.youtube.com/watch?v=6h150ksGeME

It also looks like your head/upper body "collapses" towards the ball toward the top of the back swing then even more on the down swing, kind of like leaning into a hockey shot. I suffer/suffered with this and I/my coach broke it down into 2 stages. First work on maintaining height in the back swing by "feeling" like your right shoulder slightly raises (that's what it felt like to me to create the correct outcome it might not be the same for you.) You may need to practice this in a mirror to see what it "feels" like.

Then the second stage is to maintain the height in the downswing, I lost height because my back leg knee collapsed as I rotated round (which also forced my hands away/around my body which created an out to in path). I am currently working on this by driving my back hip round and up (it feels like I am pushing up and away from my back foot, like my right butt cheek is coming round and up). The feeling of this is similar to underarm throwing a ball high in the air from your golf stance, in order to do this your hips will rotate round and up to help generate the height. I then try to create this feeling in my swing.

I think the L -to-L drill might help you, it is a great drill for learning about moving the club through the impact zone: https://www.youtube.com/watch?v=6oT3tMb5U2E

As I said I am no expert so I would recommend going to see one!