If the car can hardly turn without swaying really bad then I would cheak out the swaybar link bolts front and back. May evan be bad struts?
Don't know if this may be but what about the rear panhard bar. If that was bent would that cause things to be all over the place??
If you push down on a corner of the car and bounce it up and down then let off does it keep moving up and down for a while or does it stop after 2-3 bounces? If it stops and seems good and stiff then I would think the struts and shocks are ok.
94 T/A LT1 T56, eagle crank and rods, 30 over, LT4 hot cam kit, beehive springs, electric water pump, aluminum DS and almost all bolts on possible.----------SOLD----------------