Side-to-side shutter

I have a 2000 Impala with 215000 miles and it keeps on running. It has developed a side-to-side shutter and only happens during accelleration. It smooths out once I stop accellerating. I have had a left rear wheel bearing replaced hoping this would solve it. Not so much. It feels like it is coming from the rear of the car. There is no movement in the steering wheel. Could this be motor mounts? Any ideas would be appreciated.

Could several things.

Motor mounts is one…Ball-joints is another.

Along with tie rod ends, struts, inner CV joints, and a torque converter problem.

This one needs looking at hands-on. On a rack.

I’m curious, was the left rear bearing replaced just as a guess, or was it making noise and/or loose/worn?