This paper aims at designing, in the discrete-time setting and using sliding mode techniques, some controllers ensuring the tracking of desired references of lateral and yaw velocities for a ground vehicle with active front steering and rear torque vectoring actuators. The vehicle is described by an enhanced discrete-time model, recently presented in the literature. These three controllers have been designed considering the modified equivalent control method for perturbation attenuation, the discrete-time-like super-twisting algorithm, and the discrete-time reaching law. They have been tested with a simulation study using CarSim, where the three controllers are compared under parametric variations, external perturbations, and different sampling periods.