The head moving and the hip slide (if that's what you are talking about) could be associated with a poor pivot.
For me, I really need to focus on my feet and hips. That is to say on the backswing, once I feel the weight gather on the right instep (or arch) - no more shifting; just lift the arms a little and turn the shoulders. Get behind the ball. Look at video of Mike Finney.
On the downswing, the idea is the same. The weight gathers over the left instep and should not go past that point. If you continue shifting, you'll need to release early to hit the ball. Thus, once your head returns to basically where it was at address, it's, mostly, rotation. The head stays back, the left shoulder is working up and behind you. The right is driving down plane.
For wedges and short irons, I don't feel like there's a lot of head movement. Even for the driver, it seems that that Tour players only need their heads to move back 2-3" - again, they are coiling behind the ball.
In the Soft Draw video, Brian elaborates on the backswing extensively. The takeaway is a little to the inside, the hands work inside (no pop out). The arms lift up, elbows are soft and wide.
An old favorite of mine for a good backswing (with respect to weight shift) is to place a ball under the right foot, say and inch or two behind the 'pinky' toe. So the 'outer' portion of the right foot is in contact with the ball. As you shift to the right you'll feel the foot compress against the ball. If necessary, allow the right leg to stiffen some so you can pivot about the right hip.
This will likely feel very strange. But if you look in the mirror you'll be making a much more athletic turn behind the ball.
Erik