Towing a car behind your motor home adds no weight to the motor homes chassis. What you are feeling is the car pushing and pulling you around. Do you have brakes on the car or dolly that work with the coaches brakes?? If not, you might consider having them hooked up, it will help with slowing down and stopping, it won't push you around.
2021 Ram Limited, 3500, Crew Cab, 1075FTPD of Torque!, Max Tow, Long bed, 4 x 4, Dually,
2006 40' Landmark Mt. Rushmore