Character Rides In Vehicle

I have made a car in my first person shooter and am now trying to pput the player inside it. I want the player (a skinned mesh human) to be affected by accelaration and falling in the car as a rigidbody would be, but still stay in the seat of the car. Also, their hands need to stay bolted to the steering wheel, and, as the camera will be on the head of the character, the head needs to be reasonably steady. The type of colliders used do not matter much, as I have not got any yet.

I have tried using ragdolls and fixed joints, but the player tends to fall out of the car and go flying off the map, or just flap around violently in the back of the car. Also fixed joints always seem to bend and stretch slightly, is this meant to happen?

If you want an idea of the kind of effect I am lookin for, something like driving in battlefield 3 would be good: http://youtu.be/Oi-nrVc3F6E?t=23s.

Please could someone help me do this?