2005 Mercury Mountaineer rear end whine, how hard to fix

Before you do this you might want to try fresh gear lube. On Ford products they use a synthetic additive in the rear and not in the front 4x4 axle.
The next thing would be to determine if it is a wheel bearing or a pinion bearing. You have to pull the axles and eliminate them as the problem. You might get lucky and not need to do the pinion.
The technical part of shimming the pinion gears with replacing the pinion bearing is about the worst part of the job. You won't know about the gears until you see them. You will need extra shims on hand.
It is a moderate job for two people. If you have all the parts it can be done in a day.

My 2005 mercury mountaineer has rearend whine, dealer stated at last oil change that the seals were leaking, and may need replacing,also the bearings could need replacing. I took the car to another mechanic and confirmed this he said the bearings were turning inside the housing.