Multi-robot systems, particularly mobile manipulators, face challenges in control coordination and dynamic stability when working together. To address this issue, this study proposes MobiDock, a modular self-reconfigurable mobile manipulator system that allows two independent robots to physically connect and form a unified mobile bimanual platform. This process helps transform a complex multi-robot control problem into the management of a simpler, single system. The system utilizes an autonomous docking strategy based on computer vision with AprilTag markers and a new threaded screw-lock mechanism. Experimental results show that the docked configuration demonstrates better performance in dynamic stability and operational efficiency compared to two independently cooperating robots. Specifically, the unified system has lower Root Mean Square (RMS) Acceleration and Jerk values, higher angular precision, and completes tasks significantly faster. These findings confirm that physical reconfiguration is a powerful design principle that simplifies cooperative control, improving stability and performance for complex tasks in real-world environments.