Grinding and squealing noises when braking?

Once the differential starts making noise it is too late for a service but usually it will not make grinding and squealing noises. Are you sure it is not one of the rear brakes causing the problem? Can you please shoot a quick video with your phone so I can hear the noise? That way I can tell for sure what's going on. You can upload it here with your response. This guide can help you raise the car and remove the tires for inspection:

https://www.2carpros.com/articles/wheel-removal-and-re-installation

and

https://www.2carpros.com/articles/jack-up-and-lift-your-car-safely

Please go over these guides and get back to us.

I took it to the auto repair shop that did my brakes last year. They told me pads and rotors looked great. They seem to think it’s the differential. I’m not sure what the problem is. I’ll probably take it someplace else to get a second opinion about this before making any repairs. I’ve attached a video clip that was recorded from my security camera.

Thanks for the video, it helps. That sounds definitely like brake noise. Did you check the rear brakes and parking brake shoes as well? Check out the images (below). Please let us know what you find.

I was told by another auto mechanic shop that my brakes are in excellent shape. The noise is coming from the rear axle bearings.

Did they check the parking brake? To do this you must remove the the rear rotors. please check out this video of the job being done on a similar vehicle; the process is the same.

https://youtu.be/uo1RnATyEok

And this video shows how to do the axle bearing if you need it:

https://youtu.be/zarxKsspr3s

Please go over these guides and get back to us.