I noticed my rear end, when I put it in drive, the right rear wheel spins when you give it to much gas, in reverse the left rear wheel spins when you give it to much gas.

The purpose of the differential is to allow the two wheels to rotate at different speeds. Usu. in curves and the like. What you are experiencing is the differential working in relation to traction. The wheel that spins has less traction than the other and receives the most power in an attempt to move the vehicle. Ever get stuck in the mud with a vehicle that has a differential. Pain in the ass! You attempt to get traction on the spinning wheel, maybe with a board or something, and the other starts to spin. If possible, park on level surfaces and surfaces that won't pose this type of problem, like loose rocks, muddy or wet surfaces, etc. How are your tires? This may also be the culprit. Have your fluid checked, but I doubt that's the problem.

I noticed my rear end, when I put it in drive, the right rear wheel spins when you give it to much gas, in reverse the left rear wheel spins when you give it to much gas.
That's what it supposed to do. Get a posi or a locker and both of your wheels will spin at the same time.

Now that we are on the subject....does anyone have the low-down on which is the "better" unit for our Caddys? The Detroit or the Eaton. I now a number of RWD owners have gone with the Eaton. Does Detroit even make a locker or posi for the GM 8.5 inch?

I think detroit does, but it seems like its a more heavy duty application like my truck.