With the increasing intelligence of vehicles, the growing network communication load introduces uncertain time delays in control signal transmission, posing a more serious challenge to the precise tracking and synchronization control of dual-motor steer-by-wire systems. To address this problem, this paper proposes a tracking and synchronization control strategy. Firstly, a dynamic model of the steering motor incorporating time delays is established. On this basis, an Online Identification Adaptive Smith Predictor (OIASP) is designed to accurately estimate the uncertain time delays in the system. Furthermore, an Adaptive Hybrid Active Disturbance Rejection Control (AHADRC) controller is proposed, which utilizes a Phase Advance Extended State Observer (PAESO) to reduce phase lag in the observed states. Combined with feedforward control and linear state error feedback, a FF-LSEF composite control law is constructed, significantly enhancing the dynamic tracking performance and robustness against complex disturbances. Theoretical analysis demonstrates the favorable stability of the proposed AHADRC. Additionally, a mean deviation coupling synchronization control structure is incorporated to further enhance the synchronization accuracy of the steering system. Finally, the effectiveness of the proposed control strategy in suppressing uncertain time delays and external disturbances was verified through simulation experiments and hardware-in-the-loop tests.