This is a marvellous observation by good ole dad. If the centre moves backwards through the back swing, there has to be a compensatory move forwards to get back to the 'impact' position in the downswing. Also, most golfers do not swing through but actually try to hit and so the swing after moving backwards becomes a lunge at the ball rather than a swing through to the target.

All top golfers rotate backwards on a braced, slightly flexed right leg with the weight on the inner sole of the right foot. Then there is a shifting of weight onto the inside of the left foot on the down swing. Some pros use this as the signal to begin the downswing. So really there is rotation around two separate pivot points but those points were already established in the set up so effectively the centre is rotating around itself. If the centre has moved forwards or backwards from its original position at impact then the arms/hands
have to act independently and tend to rotate or tighten.

If you get a sense of 'swinging where you are' in relation to the target and a sense of the head remaining at a constant height from the ball through the swing, then you will be rotating properly. Also the ball is only to 'get in the way of the swing', not to be 'hit'.

I am only writing all of this in order to 'explain' the mechanics of it. As you have found out, once the balanced position is set the swing takes care of itself and you hit 'pure shots'. I hope others can learn from this as I feel it is absolutely vital.

GREAT STUFF!