This paper investigates the controllability of vessel berthing systems assisted by multiple tugboats under actuator faults or failures. In such interconnected systems, a failure of an individual tugboat can potentially compromise the berthing operation, or even lead to the collapse of the entire system. To address this challenge, the dynamic model of the multi-tug-assisted vessel system is first derived, followed by a controllability analysis under various fault scenarios to identify tolerable fault configurations. Then, a robust controller is proposed, integrating an adaptive disturbance observer with finite-time sliding mode control. This design ensures effective rejection of maritime environmental disturbances, practical finite-time stability, and bounded trajectory tracking errors. To accommodate different fault conditions, a switching control allocation strategy is developed to redistribute control efforts among the remaining healthy tugboats, thereby maintaining system reliability and efficiency. Simulation results under various faulty conditions demonstrate the effectiveness and robustness of the proposed control approach.