Are you making sure to keep your knees bent and relaxed?
When you're on your toe-edge your ankle/foot can function as a shock absorber, but when you're on heel-edge only your knees/leg muscles do. If you're legs are stiff and rigid it'll lead to that skipping and chattering you're experiencing.
When flat-basing and going straight you don't have to be on edge, just pressure an edge. Light pressure on an edge will keep the board straight, if you go completely flat while going fast your board will tend to pivot(rocker boards) or in trad. camber's case (catch an edge and scorpion onto your face).
As for weight shifting... I'm sure someone like Snowolf will chime in to tell you exactly what you need to be doing, but overall leaning back in a turn is a bad idea.