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The front wheels of a turning vehicle follow circles of different radii. This is what causes the tires to judder or hop upon making a slow tight turn.
Ackerman steering geometry is a solution to this problem. But the C7 incorporates little Ackerman steering. Ackerman steering geometry compromises high speed cornering.
That is, the juddering is a good thing. It tells you your car's high speed cornering is uncompromised. Instead, low speed parking lot maneuvers are compromised. I can live with this trade off.
Thus, I like the juddering. It falls into the same category of a bit of cam lope shaking at idle which indicate you are sitting behind a high performance engine.
My C6 did this too, just not on the same scale as my C7 Z06 does. I think the wide body cars tend to have more than the narrow body cars as the Z51's I test drove were much more subdued compared to what I currently experience.