Service robots have demonstrated significant potential for autonomous trolley collection and redistribution in public spaces like airports or warehouses to improve efficiency and reduce cost. Usually, a fully autonomous system for the collection and transportation of multiple trolleys is based on a Leader-Follower formation of mobile manipulators, where reliable docking maneuvers of the mobile base are essential to align trolleys into organized queues. However, developing a vision-based robotic docking system faces significant challenges: high precision requirements, environmental disturbances, and inherent robot constraints. To address these challenges, we propose a Disturbance-Aware Visual Predictive Control (DA-VPC) scheme that incorporates active infrared markers for robust feature extraction across diverse lighting conditions. This framework explicitly models nonholonomic kinematics and visibility constraints for image-based visual servoing (IBVS), solving the predictive control problem through optimization. It is augmented with an extended state observer (ESO) designed to counteract disturbances during trolley pushing, ensuring precise and stable docking. Experimental results across diverse environments demonstrate the robustness of this system, with quantitative evaluations confirming high docking accuracy.