John,
In my experience, if the rear end of the car has sideways movement one direction when accelerating and the other direction when decelerating it usually means the rear axle is "steering" the car. One side or the other is moving forward when accelerating and moving rearward when decelerating. This could be caused by several things; Loose u-bolts (which you tightened), broken or missing center bolt in the spring (this bolt holds all the leaves in their proper locations and also helps to locate the axle in relation to the spring, loose pins & bushings in the ends of the springs, a broken main leaf in the spring, or a broken/cracked front spring hanger/outrigger.
The panhard bar keeps the car body/chassis from shifting over the axle when cornering but has little to do with sideways movement when going straight, and should not be affected by accelerating or decelerating.
Hope this helps,
Dave