Such controllers exist, I saw several the other day at a nearby theme park. As far as building one, I'd look for a transmitter with a secondary controller input jack. They're usually used to in RC aircraft transmitters to allow an experienced pilot to teach a newbie how to fly. If your car transmitter has such a port, you'd be able to quickly unplug the wheel setup and use the controller normally.
As far as building one, you'd mostly need to figure out what the transmitter is expecting for control signals. Assuming it's an analog input, you'd only need to match the pot values for the steering and gas/brakes. You could concievably split the gas and brake the same way as is done with PC controllers.