Sounds like no need to take it off the truck since you are towing a car. You should practice taking it off and on but that can wait until you have a nice open level spot to practice and are under no need to rush. People have different sensitivity to rocking. When we have our camper off the truck we don't find any objectionable movement. Others may have different sensitivities. I suggest that when you are able to have it off the truck, try it out and see if you are bothered by any movement you might experience.