2001 Buick Regal GS supercharged, 80k miles
At 35 to 40mph the car wobbles, "only under a load" traveling downhill with no load it's fine. It's not RPM dependant, under a slight load it will shake at 35 to 40 in second gear or overdrive. No unusual sounds from cv joints. I have rotated the tires, looked at cv joints, lower motor mounts look a little weak. This wobble is felt thoughout the car.
I have not taken it to a dealer yet as I have spoken with a few and they seem confused.
Thanks so much for any help
PS the engine seems to be very smooth and doesn't miss a beat.
I have since taken the car to a tire shop and mechanic, they checked tires,wheels,front end. I now have new motor mounts and driver side CV with no change.

 

It sounds as though it could be an ignition problem. Perhaps bad plug wires or a bad ignition module. Note that vibrations might only pass from the engine to the rest of the car when the torque clutch converter engages and the vibration might even out at higher speeds, which could explain the 35-40 mph window. Check to see if you're getting a spark to all cylinders.

Please let us know what you discover.

 

I had the same thing. turned out it was the struts. the nut that held them into the canister came loose and allowed bthem to wobble like the wheels were gonna fall off.