This paper proposes a traction control system (TCS) that uses a sliding mode wheel slip controller and a PID throttle valve controller. In addition, a yaw motion controller (YMC) is also developed to improve lateral stability using a PID rear wheel steering angle controller. The dynamics of a vehicle and characteristics of the controllers are validated using a proposed full-car model. A driver model is also designed to steer the vehicle during maneuvers on a split ${mu}$ road and double lane change maneuver. The simulation results show that the proposed full-car model is sufficient to predict vehicle responses accurately. The developed TCS provides improved acceleration performances on uniform slippery roads and split ${mu}$ roads. When the vehicle is cornering and accelerating with the brake or engine TCS, understeer occurs. An integrated TCS eliminates these problems. The YMC with the integrated TCS improved the lateral stability and controllability of the vehicle.