Q: Rear differential problem?

In my experience, I have never observed the differential to be the cause of vibration. The most likely culprits are the wheel or tire, driveshaft, or axle. You had the wheels balanced, so that will rule out balance or a bent wheel. A broken belt in the tire could cause this, and unless the shop used a "road force" balancer, it might go undetected.

Try rotating the tires front to back for verification. A bent axle can be spotted by spinning the rear wheels off the ground. U-joints and the drive shaft are a little more involved to check. The best way to check for a bad u-joint is to remove the driveshaft and check that move freely and smoothly. If they are tight, or rough, they’ll need replaced.

The only way I have found to check the balance of a driveshaft is to try another one, or have a specialty shop check it. They are balanced at the factory by lightly welding on small tabs of steel. Sometimes they come off. You can usually spot where they were. If the tab came off, it will need to be rebalanced. One more thing to check is the engine and transmission mounts. If they are broken, the driveshaft angle will be incorrect and can cause a vibration. Go ahead and have this checked one more time and make sure that all of these items were covered. If you would like another opinion on the car, a certified technician from YourMechanic can come to your home or office to diagnose the vibration for you.