I have a 2012 GMC Terrain and have experienced the "wobble" 5 times. I decided to change my procedure to new recommendation. Bought a RVI Towed battery charger and decided to have it installed in Bradenton, FL where we were staying for the winter. I also bought an adapter by Blue-ox that has a switch to tow or not tow. Basically it turns off the anti-skid. Also had to buy a new 7 to 6 umbilical cord to wire from MH to car. It all worked OK when I started out. Next day did not work and I had a dead battery. I switched back to old procedure of just removing fuse inside car. All together cost was about $450.
I called RVI and I did all of the things they recommended but no success. They sent a new charger. Same story.
I finally figured out that the ground from the MH to the Car would work the turn signals and the brake lights so I knew that I had a ground to the car. So I bought a 14awp wire about 8 foot long and wired it directly from the receiver that is plugged into the umbilical cord to the negative pole of the battery.
At this time it is working and I think that I have solved the problem.
Hope this helps someone else