This paper focuses on the research of longitudinal and lateral instability of dual motor electric vehicles during driving. The main objective is to ensure that the vehicle maintains both longitudinal and lateral stability during acceleration and steering, and also to ensure dynamic performance. The study involves the design of a drive anti-skid steering control system and a handling stability control system, with coordination between the two. To achieve this, the study analyses the vehicle’s different performance and stability requirements at different speeds. It sets a speed threshold where performance is prioritized at low speeds and stability is prioritized at high speeds. Based on these requirements, the activation conditions of the control system are designed for different speed ranges. Results from simulation verification under two different operating conditions - acceleration and steering - show that the control systems can effectively manage wheel slip rates to stay within 0.02 of the optimum slip rate for the road surface when the wheels slip. In addition, the deviation of the actual yaw rate from the setpoint is kept below 16% of the setpoint when the vehicle is experiencing lateral instability. The control strategy developed not only improves the stability and dynamics of the dual-motor electric vehicle but also has academic implications for improving vehicle stability and dynamics in general.