Rob, I may be of no help... but I often have much the same problem... when I mash the gas, the car just goes to the right... then the left... then the right... then the left and sometimes in big circles... and smokes something fearce... then all seems fine after I let up on the gas... but sometimes after doing this test, it makes me see flashing red lights... must be from breathing all that smoke or something? Haven't quite figured that one out yet...
Is that the problem your having too? I know Q often has similar problems...
Seriously though.. sounds like the rear is either shifting, and or as suggested not set square or properly. I'd take a good set of measurements such as Brent suggested, and then between front and rear tires on both sides... perhaps the rear is angled slightly (one side more forward then the other) Or maybe it is shifting or moving slightly?
Let us know what you find? I guess I'll just have to learn to live with the problem I'm having on mine...