[2003eclipse]

My buddies 2g FWD did the same, in the rain. There was a bushing in the upper rear suspension that was shot. Burned it out, pressed in a new one and the whole feeling of the ass end swaying side to side going straight down the road went away. So it happens to FWD also.
Just jack the car up one side at a time and do a shake down test on the tires. Check for loose ball joints/ bushings. Good Luck