<p>Uncrewed underwater vehicles(UUVs) play an indispensable role in ocean resource efficiency utilization due to their security and cost-effectiveness. However, the significant uncertainties, time-varying disturbances, and unstructured subsea environments pose challenges for UUVs in achieving precise and efficient marine missions. To address these challenges, this study introduces a novel cooperative control framework for UUVs. The proposed framework minimizes the high control efforts of sliding mode control while preserving robustness, enabling efficiency and precision for long-duration dynamic hovering missions of UUVs. Specifically, a key innovation is the development of a deviation separation strategy, which, for the first time, decouples hovering deviations into task-specific and anti-disturbance components using an influence function. This enables real-time disturbance estimation without prior knowledge enabling adaptive disturbance compensation. By cooperating between LQR and SMC, the proposed method avoids the performance conflicts commonly observed in single-controller schemes. This structure improves compensation accuracy, robustness to disturbances, and energy efficiency across various operating conditions. The results demonstrate that the proposed cooperative control strategy effectively counters current perturbations by leveraging the real-time insights from the error segregation, while concurrently executing high-precision hovering tasks with low control costs. This work advances UUVs control, offering a versatile solution for complex underwater tasks.</p>