The low-orbit satellite communication can provide users with low-delay and ultra-wideband communication services worldwide. By the wide available bandwidth and immunity to interference, free-space optical (FSO) feeder links are presented as an ideal alternative to radio frequency (RF) feeder links for satellite-to-ground backhaul, and the space-ground integrated optical network (SGION) is gradually formed by using FSO feeder links to integrate the low-orbit satellites and the terrestrial optical network (TON) for backhaul services. The propagation channel characteristics of FSO feeder links vary significantly during low-orbit satellite passes, and atmospheric turbulence causes serious scintillation in FSO feeder links at low elevations, increasing link budget and restricting link capacity. Limiting the observation range of optical ground stations (OGSs) to the high elevation area can establish high-capacity feeder links to improve SGION’s throughput, but inevitably increase the network dynamics and reduce the satellite visibility. This paper trades off SGION’s throughput and dynamics by planning FSO feeder link handover and capacity adjustment. Two baseline schemes and the feeder link handover and capacity adjustment scheme based on non-dominated sorting genetic algorithm (NSGA-FLHCA) are proposed. By finding the Pareto edge of the multi-objective optimization problem, NSGA-FLPCA is more effective in improving network throughput and reducing network dynamics compared with two baselines.