If you can, raise each rear wheel off the ground. Grab the tire at the 6 and 12 o'clock position and push pull to check for play. Do the the same thing again at 9 and 3'clock position. Do this for each wheel. You need to check for play in the wheel bearings, and check for play in the suspension itself.
If you find nothing, rotate your tires to the front to see if the shaking follows the rear tires.
If the rear end still shakes, I would look at the possiblity of warped unbalanced brake drums.
If the front end shakes now after the rotation, find another tire shop to balance your wheels.
1997 Pontiac Bonneville SEi-SCRAPYARD
2000 Chevrolet Blazer LT 4X4 4.3L
2002 Chevrolet *-10 LS Ext Cab 4X4 5.7 V8