Currently, LEO satellite networks enable global connectivity and emergency services, yet face dynamic topology changes and resource constraints. Traditional routing struggles with orbital dynamics and latency-sensitive demands. To address challenges related to data processing and transmission efficiency in dynamic satellite networks, this study proposes a hierarchical satellite routing architecture that decouples the roles of computing and communication satellites, enabling resource specialization and self-organized management. Additionally, an active edge caching mechanism is introduced, significantly reducing redundant data transmissions and processing delays across the network. Furthermore, the paper develops a deep reinforcement learning framework that integrates intelligent weight analysis to optimize packet routing decisions. Experimental results demonstrate that the proposed method achieves superior performance in terms of average delay and task completion rate compared to traditional approaches, with even greater advantages observed upon the integration of mobile edge computing.