We have gone through all the options including a flatbed trailer, tow dolly, and finally a four down tow-bar setup. The four down tow is much better than any other solution. I see a listing for a Chevy Lumina on this fit-list of base plates.http://www.remcotowing.com/fitlist.pdf
You will need a base plate to fit your make/model of car, a tow-bar that attaches to the RV hitch receiver, a brake light wiring kit, and optionally a brake system. You might also need a electric pump installed on the tow vehicle that circulates the transmission fluid and keeps things cool while being towed. Or a drive shaft dissconnect installed.
We have a 40' RV towing a Mercedes ML 320 SUV, they said it was not possible to tow this vehicle since it is all wheel drive and not able to disengage the transmission from the wheels. I saw another member on this forum uses the same setup with a ML-320 and so I knew it was possible. A small nightmare getting it installed because there are a few difficult things that have to be done, like plumbing the electric pump into the transmission pan, and getting a 12+ signal on the brake by installing a switch on the brake pedal. BUT, After all the problems it is the best system for sure. You can stop and disconnect your towed vehicle in minutes and re-attaching is also quick and easy. No tow dolly to worry about, no extra trailer to have to park, no extra license plate and costs. I opted for the Blue-Ox braking system, it will stop the vehicle in an emergency, like if it disconnects from the RV or if you need to stop really fast. Maybe more than you want to spend but it is cheaper than a flatbed trailer, and more convenient than a tow dolly. Good luck on finding the right solution for you.