Differential problem

I think I'd get a second opinion first before I'd spend that much money. If you have a locking back axle, (GM used to call that "Posi-traction), they have clutch plates that can chatter when the two rear wheels turn at different speeds, which means turning corners. Ask at the dealership if they have an additive for those differentials. Dodge trucks can make a chattering noise if the gear lube is replaced and a small bottle of additive with whale oil is not added. That is required to modify the friction of the plates to prevent noises. Yours may be similar.

If something is coming apart or wearing excessively, that additive won't fix that. Differentials are very tricky to set up and adjust properly to prevent wear and gear noise so most mechanics replace the entire axle with a used one. It is customary to remove the rear cover first to inspect the gears and bearings and to check for metal pieces breaking off. Listening for the source of the noise will lead him to the differential, but it should be inspected first before replacing it.

The best way to approach the second opinion for this type of problem is to not mention the first diagnosis. Describe the symptoms and related observations in as much detail as possible to speed up the diagnostic time, but let the mechanic come to his own conclusion.

When a customer says, "I was told it is... ", The mechanic is naturally going to go there first and potentially overlook some other possible causes. When he is starting from scratch he will go through a series of checks, probably including a test-drive, and will look for all the common stuff first to rule those out.

If the second person comes up with the same diagnosis you may get different repair estimates. As I mentioned, setting up axles is a tricky job but it can be done with the right special tools, service manual, and experience. Most independent shops don't have the special tools. Most mechanics will elect to install a used axle assembly from a salvage yard. That will be faster and less expensive for labor but you will have the same used axle as you had before the noise started. If this is a known high-failure part your mechanic will probably want to repair it with new internal parts to make it better than a used one, provided he has the confidence that he can do a good job. He knows there's no point in installing a part that is likely to develop the same problem in the future.