This paper presents a novel hierarchical control architecture designed for navigating multiple tugboats to perform complex maneuvers, including approaching, enclosing, and capturing a large target vessel, while taking into account external disturbances and operational constraints. The proposed hierarchical control architecture includes a high-level nominal controller for trajectory generation, tracking, and coordination, and a low-level model-following controller for multitask execution. The low-level controller integrates constraint-driven control to refine nominal control inputs generated by the high-level controller, and local control to mitigate disturbances. To achieve multitask execution across all phases, the constraint-driven controller activates only essential constraints, enforcing seamless maneuver transitions without relying on ad-hoc controller switching. Specifically, we design constraints to facilitate effective enclosing behaviour while guiding the tugboat fleet toward the target in formation. We also adopt a so-called Prescribed-Time Safety Filter to enforce mild contact with the surface of the target vessel within a specified finite-time interval. Simulation studies validate the proposed control architecture across all maneuvers throughout the operation and demonstrate its capability to achieve complex multi-tugboat coordination.