You have several problems going on with this design. From what i can see in the attached pictures, the big plastic screw draws back on the ali wedge which in turn acts on the rubber block, clamping the unit. The trouble is, that rubber block has 2 slots in it and i susspect that is where the weeble wooble is comming from. As you are traveling down the road, the whole frame is going to move due to wind, road conditions, bad driving
ect and the whole frame will start to resonate at a frequency. This is going to cause stress in the welded joints and if it gets to a certain point, fractures may occure.
To analize the design better, i would need to know the dimentions of the rack as well as the bikes, materials and weights.
Ian