Your car does not have struts for the rear - it has shocks. The auto parts store should have been able to tell you that. The back end being bouncy and kicking out like that is a good indicator of bad shocks. A need for a 4 wheel alignment will also cause the side stepping, but not the bouncing.
The steering position sensor is the mostly likely cause for the service stability system warning on the DIC.
Edit - After reading Toasty'* and Darcy'* posts in your other locked thread http://www.bonnevilleclub.com/forum/...ic.php?t=84428
it reminded me of something. Do these events coincide? Does the service stability system warning come on after hitting a sharp bump, or does it happen at any time? Before I changed my rear shocks, if I hit a sharp bump with the right rear, it would set that warning. Having the car scanned, as suggested, is a good idea to find out what is happening
Black 2000 SSEi, Silverstar Headlights, Angel Eyes fogs, 3rd brake light overlay, hi-flo cat, drilled 180 degree thermostat, Intense FWI, PCM, shift kit, and 3.4 Pulley. Solid front mount.