<p>Underwater robotic systems are increasingly expected to operate in confined, unstructured, and dynamic environments, in which conventional rigid vehicles and manipulators face limitations. To address these challenges, we develop a hybrid reconfigurable flexible underwater manipulator that integrates rigid self-propulsion modules with modular soft joint modules, enabling efficient thrust-based locomotion and highly maneuverable snake-like motions. The proposed architecture allows the robot to reconfigure its motion patterns in response to diverse operational requirements. Accurate kinematic modeling of such systems is critically dependent on the representation of the soft joint deformation. To this end, a novel soft universal joint (SUJ) model is proposed, which remains valid under non-constant-curvature (CC) bending and large-deformation conditions. The accuracy and generality of the proposed model are then evaluated through comparisons with the classical CC model. Building upon the SUJ-based kinematic framework, a priority-based control strategy is also developed to coordinate primary trajectory-tracking objectives with secondary safety-related constraints, including obstacle avoidance and joint-limit protection. Subsequently, numerical simulations and water-tank experiments, encompassing spiral motion, pitching upward, linear motion, and obstacle-avoidance tasks, are conducted to validate the proposed approach. The results demonstrate that our method achieves significantly higher accuracy than conventional CC models, while the control strategy also ensures robust task execution under multiple potentially conflicting objectives. Overall, this work presents a flexible and reconfigurable underwater robotic system with experimentally validated modeling and control methodologies, thus advancing the capabilities of underwater robots in complex and constrained environments.</p>