If there is a difference between turning left and right, the difference must be in the geometry of the shafting. I would turn the rig right as much as to make it chatter as though in use and take a picture of the hitch setup from overhead. Then do it for left and compare the images. The comments about angles of the U joints below are also important. If the rear joint of the shaft stays pretty straight, the front joint will cause rotational vibration when it allone is bent. (has to do this unless it is a CV joint.) If the joints at opposite ends of a shaft are bent in opposite directions when flexed (as is the drive shaft in a live rear axle car when loaded or going over a bump) the Ujoints must be set up so the yolks on the shaft are aligned with each other, and the yolks on the driven components (front input shaft, and differential flange) are aligned. This setup cancels the rotational accelleration/decelleration. In a shaft with both joints being bent in the same direction (as a machinary shaft with a pulling pivot near the center of the shaft length) the opposite is true. the yolks need to be 90 degrees out of phase so the accelleration of the fromt shaft decellerates the output. The illustration and info does not include a shaft bent with both joints bending non parallel as I have added to the discussion, but it should make clear what I am saying. One other issue might be how sharp you turn left or right.
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