I would suspect shocks as well. Their job is to keep the tires on the road. Comfort is a secondary consideration. Mine would leave the road on an onramp curve if it hit a bump. Disturbing to have your back end jump sideways 6 inches at 50 mph. New shocks solved that problem. now the same bump on the same on ramp at the same speed and my back tires are firmly planted.

 

Alignment was pretty far off,, thanks! The clutch has been replaced a few months back so the torque tube back has been disassembled. this means the lower A-arm mount has all been out and probably put back together and the system has some slop in it (doesn't bolt together to the exact same place on the frame. This leaves a lot of room for a bad rear alignment.

 

I guess I'm resurrecting an old thread.
I just now came across this.
I've got an 02 Conv stock everything.
Drove it to Amelia Island Concourse D'Elegance from NJ last March.
Drive down was perfect, nice comfortable drive.
But, my auto trans died 2 days after I got there.
Had new(rebuilt) GM trans installed at local Chevy dealer.
I could not wait around for repair to be completed. Flew home and had car shipped back.
After getting the car back I noticed it was driving as others described in this thread. It was kind of wandering at highway speeds. For awhile I tried to ignore it, UNTIL my wife asked if it was very windy-I asked why do you ask. She says it feels like the car is getting pushed around from side to side. That was it. Now I had to get it checked out.

I had car re-aligned. I was told it was slightly out of spec and was told that would not cause what I was describing. New alignment did not make it better. Next, I replaced tires and wheels with the tires & wheels from my 03 Z06. No real change. Next brought it into local Chevy dealer. They said they could find nothing wrong. But, they did not drive it on highway at speed.

Next step is to have my buddy check it out. He's a former GM Master Tech. Has his own shop and is the head tech for NASA NE Racing. He builds and maintains road race cars in addition to routine wrenching. I told him I was going to replace shocks & sways. He said-Don't Do Anything Till I Check It Out.
But, 1st he's going over my track Z06. Once that's done & put away for the winter he'll get to my 02 convertible.
To be Continued

 

Had the same exact issue,
first look at your tires, thread and pressure (and i mean it)
2nd look at your rear stabilizer links, any lost component at that area will cause havoc
3rd visit a shop for alignment, and thats after you make sure the 2 points above are done