Rear Differential Replacement

I have a '98 Subaru Legacy Outback. About a month ago while I was on a trip my rear differential went out . I took it it to a Subaru Dealership and they installed a brand new stock replacement.

I hadn't even driven a thousand miles on it and I heard a winding noises when accelerating and decelerating. I took it to my trusted Mechanic, the owner of a certified Napa Autocare Shop, and had him look at it. He said it was my rear differential and let me feel it. It was burning hot after 15 miles of driving and the oil from in it was burnt completely black. His diagnostic read that the rear differential appeared to be installed incorrectly and recommended that it be taken back to a delership for warranty repair.

I then took my car to the local dealership in my area and had them look at hoping that my warranty would cover any issues. The Dealership tells me that there is nothing wrong with my rear differential. They say that my AT light is flashing and my central differential/transfer case is where the issue lies and that is where the noise is coming from.

I have discussed this with my mechanic and he said that regardless of the status of my transfer case, my brand new rear differential should not be getting that hot and the fluid should certainly not be burnt.

I have my mechanics diagnostic in writing and am on my way to the dealership to get a written diagnostic from them stating that my rear differential is in perect working order.

Any advise, thoughts on what my legal stance is here?

Any advise, thoughts....