The time-varying characteristics of Low Earth Orbit (LEO) satellite networks and the unbalanced distribution of ground stations pose severe challenges to network robustness optimization and efficient traffic management. To address these issues, this paper proposes a LEO satellite key node evaluation algorithm fusing multi-dimensional spatiotemporal features, aiming to accurately identify the key nodes that maintain efficient communication between ground stations. The algorithm constructs a time-varying topological graph based on the two-layer interaction between inter-satellite and satellite-ground networks, designs a multi-dimensional node feature system from the perspectives of local structural attributes and global dependency relationships, and establishes a multi-dimensional spatiotemporal feature extraction model by integrating Multi-Layer Graph Convolutional Networks (MLGCNs) and Long Short-Term Memory (LSTM) networks. This model captures the spatiotemporal evolution law of the network and completes the node importance evaluation. Simulation results show that the proposed algorithm has significant advantages in both the accuracy of evaluation results and temporal stability; implementing a traffic diversion strategy based on the key nodes identified by the algorithm can effectively alleviate network congestion in high-load scenarios, providing a new research idea for the load optimization strategy of satellite networks.