Container transportation is pivotal in global supply chains, facilitating the exchange of goods between companies across different countries. Given the exceedingly high operational costs of transporting containers, optimizing itinerary schedules can yield significant benefits for logistics companies. In this paper, we delve into a real-world container transportation routing issue where trucks are scheduled to haul trailers, subsequently transporting containers amongst container depots, ports, and warehouses. Our research bridges the existing gap between academic literature and industrial practice by examining the versatile role of trailers. We specifically focus on factors like trailer capacity restrictions and the ability to detach. To encapsulate these intricacies, we introduce a mixed-integer linear programming model, incorporating new variables, invariants, and constraints pertinent to these requirements. We follow this with the proposition of an Approximate Adapted Large Neighborhood Search algorithm (A-ALNS) aimed at solving the model. Within this algorithm, six innovative operators and elimination strategies have been integrated to amplify the efficiency of solution searches and sidestep local optima. Moreover, we've established an adaptive scoring mechanism to expedite operator selection and deliver feasible solutions within constrained timeframes. Our empirical tests on 25 data sets underscore the efficacy of our algorithms; they serve between 90.9% to 100% of total requests across all instances. Impressively, our proposed framework can attain feasible solutions within an hour - a task that often spanned days with preceding methodologies.