No, no. You don't understand how steering works in a real car. It does NOT work by the car tyres being turned to lie on the tangent of the circle of turning.
In a turning car, the tyres are always slipping. The slip-angle determines the sideways force of the road onto the car, and that is what makes the car go round the circle.
Putting more drive on one side than the other will TURN THE CAR, but leave it going in a straight line. It's called an oversteer skid. The way that the car nose points through a corner has very little in principle to do with the way its CofG actually moves. Similarly, the restoring-force on the steering-wheel (aka "feel")has no relation to the amount of grip available.
Its pretty much the whole art of car design to make all these effects feel to the driver as if they are the same, so that the car becomes driveable. Colin Chapman's book is an excellent introduction.