front wheels schudder/crab walk when turning
For starters, check the tire pressure. If that’s within spec, have the alignment checked. The traction control could be malfunctioning. Any warning lights on?
IIRC, that model was available with AWD.
If the OP’s CTS has AWD, I think that the problem is likely to be related to the Center Viscous Coupler.
And, if it is indeed an AWD vehicle, I have to wonder whether the tires have been consistently rotated on schedule, and if they are equally-worn. Tire mis-matches are the usual source of excess wear on the Center Viscous Coupler.