It may be a waste of $10 bucks(or less) but try adding some antichatter additive to the rear diff. I had a shudder after towing heavy say 50 plus miles and anytime on left turn from a stop. I had Amsoil75w90 Severe Gear oil in it. I checked u/joints and angles etc. I bought some generic anit chatter additive at a parts store. Put it in and no more shudder after a few miles of driving. These AAM diffs are not suppose to shudder or need additive bvut I found old posts talking about the same thing. Its worth a try.