I would start here by checking to see if your tow dolly has lights. More than likely it does, and you can plug the 4-way on the dolly into the 4-way on your motorhome. This would take care of your light problem. You will not be able to plug the 4-way on your 2012 Mazda 6 into the 4-way on your motorhome to power the lights.
If your tow dolly does not have lights, I recommend using magnet lights like the Magnetic Tow Lights - Red LEDs - 4-Way Flat Connectors - 20' Long Harness # PE26UR.... view full answer...