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Is there adjustability in the angle of the control arms? The control arms are short so slight changes in the angles result in exaggerated axle movement under travel. As you jump on the throttle the torque wants to roll the car to the right, compressing the right rear suspension and lifting the left side. This is causing your rear end housing to change angles. In your case it sounds like the right rear is being extended while the left rear is being pulled. If you can adjust the angle of the control arms you can adjust some of this out.
Of course, I would double check the alignment and for loose parts as well. But, you sound like the pull is dramatic so I think it's the control arm angles, and length. The suspension design you are describing is a Satchel Link. This is used in a lot of circle track cars because it can be adjusted for "rear steer" and can be designed to help the car turn.
Be careful!
I'm not an expert, just my thoughts.
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