Rear differential jerks

Hello, I am Danny.

Just a quick question. Is your vehicle front-wheel drive or all-wheel drive?
Danny-

It is an all wheel drive. You did not give me that option do. I chose 4wd.

Here is my video.

Hello again.

It sounds like you may have the noise coming from the rear u-joints mounted on the rear driveshaft. U-joints are a replaceable part that are subject to normal wear and tear. It is kind of hard to diagnose sounds via email as opposed to not hearing/seeing the symptom in person at the vehicle. The best way to diagnose is to have the vehicle put up on a vehicle hoist and physically inspect all suspension components and related hardware to visually look for any damage/wear/noises etc., including the u-joints. I have attached a tutorial for you to view. Hope this helps and feel free to ask any questions if needed. Danny-

https://www.2carpros.com/articles/how-u-joints-work

Hello again.

Sorry I just replied before seeing your video! It looks like you have a damaged/missing rear differential bushing. That is a bushing used to mount the differential to the frame/attaching point. You can clearly see the "clunk" when shifting the transmission into gear. I will look up a diagram for the related components and get back to you. So glad you could send the video, makes it a lot easier!
Danny-

Hello again.

Here is a picture of the differential mount bushing your vehicle is requiring. Apparently it uses a special installation tool to press the new bushing into the differential mounting point. Any local shop would be able to do this repair. I would recommend having this repair done as soon as possible to prevent any further damage especially to the drive axles. Hope this helps and feel free to contact if any other questions come up.
Danny-