2002 Ford Explorer Noise and Rattling from rear during acce

Hello,

(2) weeks ago I bought a 2002 Ford Explorer Ltd. V8 from a local dealership. The first time I drove the car longer than (15) minutes I noticed a rattling, vibration noise coming fronm what appears to be the right rear. The sound only occurs when the car has been sufficently driven and during accelerating and turning the wheel (i.E parking maneuvers). There is no sound when the car is cold. I brought the truck back to the dealer who first said he changed the fluid in the rear diff and added an additive. He said that corrected the problem. I was concerned that this was a cheap quick fix, so I sent him the Ford TSB 06-4-4 (Limited Slip Axle Chatter.). He then said that it isnt a "123 problem" and he'd keep it over night to check it out further. Next day he said he isolated the problem and it was that the parking brake shoe had come off and was causing the noise (he showed me the worn part). I was not happy with the solution but he said it was fixed so I took the car home again to find that the exact same problem still exists. Now I brought the truck back for a 2nd time and have been told that he is taking apart the differential and intends to replace any worn parts. My question is what should be done to the car and what should I ask the mechanic concerning this issue? I don't want to be left holding the bag when the warranty expires.