Ok. We took it to a shop, the guy says driveline/u-joint and sticking brakes. Hopefully he will not rape my mom on prices.
The transfer case does not stay locked in 2WD. However, the driveline is still spinning. Has your mom had any brake vibrations while driving/braking? The early 1gen tundras had a TSB that fixed brake vibrations.
Do you have a link to the TSB by any chance? I would really like to see it.