The flexible rail drilling robot is attached to the surface of an airplane using vacuum suction cups to perform automatic drilling operations, which is crucial for improving the efficiency of aircraft assembly. The large-span dual flexible rail system typically utilizes a dual-drive setup to maintain the orthogonal characteristics of the H-shaped structure and ensure sufficient power. The accuracy of its motion is key to ensuring the precision of the hole positions. This paper presents a modeling method for the rigid-flexible coupled dynamics of the dual flexible rail drilling system working on curved surfaces. It is a three-degree-of-freedom model, considering the robot’s movement on an aircraft surface, the center of mass position changes due to the robot’s load movement, gravity effects, and constraints imposed by the dual-drive system’s transmission method. Additionally, the paper proposes a composite adaptive control method using cross-coupled control strategies to ensure robot motion tracking accuracy and the maintenance of the H-type orthogonal structure of the dual flexible rail system. The proposed algorithm accurately estimates uncertain parameters under the influence of complex working conditions, meets synchronization accuracy requirements, and ensures parameter convergence and system stability. It combines an online parameter adaptive algorithm to solve the parameter uncertainty problem and a robust control algorithm to handle unmodeled dynamic characteristics and external disturbances. Finally, the paper designs a simulation comparison experiment to verify the effectiveness and superiority of the proposed control strategy.