Maybe there's something unique with my GC. It's a hemi powered '17 TrailHawk. The wobble seems very similar to the Cherokee - typical scenario is: Sharp left turn from a dead stop, some minor pavement dip or hump (once over a railroad crossing) then immediately after straightening out the wobble starts and the only way to stop it is come to a full stop, then start off again - somewhat annoying to anyone following, I reckon!!
I rang up FCA customer assistance today and the nice young lady was very familiar with the issue on the Cherokees. She started a new case for me so I'll letcha all know what happens.
Edit: Just heard that FCA made a change to the electric power steering starting with the 2016 GCs, so that might explain why dons2346 doesn't have a problem. What year is yours, cwswine?