On my 2001 Blazer LT I get a violent steering wheel whip/wobble. When I swerve to miss an obstacle in the road it does an exaggerated dive. Too counter this the wheel does a dive in the opposite direction. This continues to amplify until it takes some muscle to get it under control.

Just about every thing in the suspension has been replaced; front wheel bearings, all the ball joints, idler arm, sway bar bushings and all four shocks.

The springs in the back are almost flat. Could they or the rear stabilizers be causing the problem? I just like this icon.

 

Could be upper and or lower control arm bushings. Could be a bad rear spring bushing, or broken shackle. Just have to look around. If it's as bad as you say, it shouldn't be too difficult to find the problem.