As you might expect VW does not want to repair anything that still "works." They do not seem to be very concerned with whether it works optimally or as designed. As best I can tell, the CPO warranty is good, but do any of us really know what it covers. I for one, have never seen a CPO contract. My dealer enters the problem/solution in the computer and the VW computer comes back and tells them whether VW will pay or I have to pay. Thus, the deck is stacked against you. Knowing this, I personally would be willing to pay for the diagnostic time if they would inform me what they were looking for and what the final solution would be under the different possible findings.
I had fits with my transmission while under CPO. It shifted horribly and destroyed the refinement embodied in my Phaeton. I was told this was normal, which I knew was not right - but what could I do. I was getting ready to part with the car and really did not want to. Eventually VW replaced the transmission when it slipped and went into limp mode(error code left). My CPO Touareg has an alternator growl that is horrible when cold and possibly tolerable when warm. I am also getting the same stuff. This is normal. This is slight. I've never had an alternator make this much noise and I'm embarassed to drive people in the car. It bothers my wife so much, she is pushing a little to get rid of it and it's her car. However, does the alternator work? Yes and that's all VW needs to know.
VW has their business model and it seems to work as they are the biggest automaker in the world. So I don't think they are very concerned about my noisy alternator or your transmission shudder. Just work with them and don't go away and hopefully they'll find a justification to solve your shudder problem.