Sounds like the rear lower control arm bushings. Here is what mine was doing (did not have cruise on) try this.
On straight highway 60-70 mph,when I would normally accelerate to pass let say, the Jeep would move to the left, and when I would go from gas on to off- de-accelerate like down hill with foot off the the gas, it would jump a bit to the right. (could be opposite movement based on bad side of bushing) You could do a wiggly pop left-right- from gas on to off at highway speed, not good especially around turn or slippery conditions.
Basically the rear control arm bushing were worn and the slots in the axle side bushing were causing the rear diff to slightly shift around and had the play caused by the relief slots.
If your's does this you can try: remove both lower control arms. The axle side bushing slots in the middle of bushing can be filled in with windshield urethane. Allowed to dry for a day or two before re-installation. This may fix it. Otherwise you have to get new control arms with the bushings already installed and fill them in or new bushings with modification of filled in and dry and find someone who is willing to & have a 20 ton press and carefully remove and install new bushings, this is what I did.
Here is a photo showing the cut away slot (relief) in the bushing that should get filled in.
36011[/ATTACH]"]
You must be registered for see images attach