I'm surprised nobody has mentioned a pusher trailer.
No electrical connections at all... the trailer is a self contained powerplant and drive motor, connected to the car with a trailer hitch.
Yes, you could do this with a simple generator and an electric drive motor that powers the two trailer wheels. The generator can then be used at your camping spot to fully charge the onboard battery when you're stopped.
The problem with most of these ideas is that the people that want them rarely have the money and expertise to make it happen. Buy a Volt, or the BMW i3 with 650cc twin cyclinder gas motor. Actually, find the EPA compliant BMW motor in a wrecking yard and use it. Or, a nice Honda generator. Here is a loud generator that should do the job with a simple 240 VAC motor:
Honda EB10000 - 9kW - 240 volt AC @ 37 amps continuous