IMO the pivot should be responding to the hitter's hand movements. Setup in impact fix, carry the club away (pivot moves as much as it wants) drive load into impact (pivot will respond as much as needed) and BOOM.
Just me though.
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I'm not a TGM or PGA certified Pro, but I did stay at a Holiday Inn Express last night
...very helpful. I've just begun seeing an AI again and one of the things he had me working on was moving an impact bag away with the clubhead--by using the pivot as opposed to my hands.
There may be a reason your AI has you doing that drill. He has seen your motion. That may be what you need to work on. Maybe he is working on Zone 1. Be careful what you work on, just based on what you read. It is much better when you have an AI in person. I am not saying he is right or wrong. But I would give the Authorized Instructor the benefit of the doubt.