This paper proposes a novel control scheme with a three-layer hierarchical structure to improve the cornering stability of the dual-motor rear-wheel drive (RWD) vehicles with the electronic differential system (EDS). The proposed hierarchical structure for the control system includes the observing layer, control layer, and actuation layer. In the observing layer, the driver model is designed to obtain the nominal steering angle, and the state observer is designed to obtain the yaw angle which cannot be easily measured. Then, particle swarm optimization (PSO) and second order sliding mode control (SOSMC) are employed in the control layer. The SOSMC part is used to design the control law to eliminate the chattering problem in the sliding mode algorithm, and the PSO part is used to obtain the optimal weights in the sliding mode surface to meet the minimum sideslip angle error and yaw rate error. The actuation layer allocates the corrected yaw moment by distributing the driving force to each independent driving wheel. Finally, the numerical tests are carried out under the double line change (DLC) maneuver. The results show that the proposed control system can effectively improve the cornering stability of the dual-motor RWD vehicles and reduce their motor power consumption.