The control goal of the vehicle platoon is to maintain the same speed and desired distance. Most current studies are based on simplified vehicle models, and the leader’s state is also rarely considered. However, under complex working conditions, such as low adhesion or curves, the lateral stability of the platoon will be difficult to guarantee, and tracking errors of desired speed and spacing may further increase. To solve the above problems, a new hierarchical coordinated control strategy is proposed. Taking distributed drive electric vehicles (DDEVs) as research objects, the upper control level establishes a stability situation assessment model according to the vehicle’s dynamic characteristics. At the medium control level, variable weight model predictive control (MPC) coordinates conflicts between longitudinal tracking and lateral stability. A correction term is also introduced to revise the prediction model. At the same time, the weight of different control objectives of the leader and following vehicle was adjusted, respectively. Torque distribution is carried out at the lower level controller. Finally, the control strategy is tested on a hardware-in-the-loop (HIL) platform. The results show that the proposed control strategy can ensure lateral stability while improving the tracking performance of the vehicle platoon.