I recently bought a 2001 qx4. The vehicle on highway speeds sways. If I’m doing 60mph and let off the accelerator the back end will slightly move to the right. When I pass the accelerator again vehicle straighten outs again, no death wobble just this.
I had the front ball joints, wheel bearings, and alignment completed.
Issue is still there, mechanic shop can’t figure it out.. said all bushings in the rear look good.
Any ideas? It kind of scary to drive it this way

Sounds like bad Panhard rod bushings, which can cause side movement of the axle under opposite loads.

Yep, Alan nailed it.

Sounds like you need rear control arm bushings - https://amzn.to/2OvCICG

Easy to test - jack it up on the frame so the rear tires are off the ground, grab the lower control arms and try to twist them. If they move much, the bushings are shot.

Does our vehicle have a Panhard? I thought it was just a sway bar back there.

I had a death sway when I bought the car. I thought the bushings on mine looked good as well. Then I twisted them by hand and found out otherwise. Find a new mechanic.