This paper presents an innovative combined control using Model Predictive Control (MPC) to enhance the stability of automated vehicles. It integrates path tracking and vehicle stability control into a single controller to satisfy both objectives. The stability enhancement is achieved by computing two expected yaw rates based on the steering wheel angle and on lateral acceleration into the MPC model. The vehicle's stability is determined by comparing the two reference yaw rates to the actual one. Thus, the MPC controller prioritises path tracking or vehicle stability by actively varying the cost function weights depending on the vehicle states. Using two industrial standard manoeuvres, i.e. moose test and double lane change, we demonstrate a significant improvement in path tracking and vehicle stability of the proposed MPC over eight benchmark controllers in the high-fidelity simulation environment. The numerous benchmark controllers use different path tracking and stability control methods to assess each performance benefit. They are split into two groups: the first one uses differential braking in the control output, while the second group can only provide an equal brake torque for the wheels in the same axle. Furthermore, the controller's robustness is evaluated by changing various parameters, e.g. initial vehicle speed, mass and road friction coefficient. The proposed controller keeps the vehicle stable at higher speeds even with varying conditions.