To address the issue of lane departure caused by human factors, a hierarchical human–machine shared control framework for lane keeping was constructed with a dual-steering-by-wire differential steering intelligent vehicle as the research object. First, the mathematical models required for the hierarchical control were established. Second, an upper-level controller for automated driving was designed, which included a single-point preview driver model that mimics human driving behavior and an MPC+MFAC (Model Predictive Control + Model-Free Adaptive Control) scheme to mitigate the influence of prediction model errors in standalone MPC on control accuracy. Third, a middle-level controller based on dynamic role-switching Stackelberg game theory was developed to realize human–machine shared driving, in which the dominant role in the game was switched according to driving risk to reduce human–machine conflict. Finally, a lower-level controller employing MPC+SMC (Model Predictive Control + Sliding Mode Control) was designed to achieve differential steering while alleviating the chattering phenomenon inherent in conventional SMC. The co-simulation results show that compared with the MPC controller, the maximum absolute value of the vehicle lateral error of the MPC+MFAC upper-level automated driving controller is reduced by 31.3%; compared with the SMC controller, the maximum absolute values of the yaw rate error and the sideslip angle error of the MPC+SMC lower-level controller are reduced by 71.4% and 66.7%, respectively; and compared with fuzzy human–machine shared control, the dynamic human–machine shared control does not interfere with the driver's obstacle-avoidance steering when the driver is attentive, and reduces the maximum absolute value of the vehicle lateral error by 81.9% when the driver is distracted. It is evident that the designed hierarchical human–machine shared controller achieves significant lane-keeping performance with minimal human–machine conflict.