Geosynchronous Earth Orbit (GEO) satellites, which can relay image data for Low Earth Orbit (LEO) satellites, play an important role in remote sensing. With the development of satellite technologies, the significantly improved computation capabilities of GEO satellites have enabled space service computing, through which GEO satellites can provide data processing services before forwarding to reduce the quantity of transmitted data. In the presence of multiple LEO satellites, how to make effective use of limited communication and computation resources in GEO satellites has become crucial. At present, the research on satellite resource management typically focuses on either communication or computation resources. Existing resource management algorithms are usually of slow convergence speed, which limits their applicability in real-time remote sensing scenarios. Therefore, we propose an aggregated resource management method for remote sensing applications. We first propose models for transmission tasks and processing tasks of remote sensing images. Then we formulate the aggregated resource management for satellite edge computing as a hybrid Stackelberg game and simplify the problem to speed up its convergence speed. Then we propose a distributed resource management algorithm to determine the optimal strategies. Simulation results show that the proposed method can quickly obtain the optimal resource allocation strategy and outperforms typical dynamic iterative algorithms in terms of service quantity and throughput.