Abstract: Group B of the 13th China Trajectory Optimization Competition (CTOC-13) focused on the design of reusable spacecraft round-trip trajectories and sequence planning between Low Earth Orbit (LEO) and a Distant Retrograde Orbit (DRO) around the Moon. This work first computed lunar departure windows from LEO and designed phase modulation control maneuvers. Subsequently, both gravity-assist lunar transfer trajectories and direct transfer trajectories from LEO to DRO were designed. For the return leg, a DRO-to-LEO transfer trajectory was designed using a backward-solving approach. To address the challenges of strong nonlinearity and narrow convergence domains inherent in DRO orbital rendezvous, a novel time-orbital cooperative homotopic control method is proposed. Furthermore, a comprehensive database of LEO-DRO round-trip trajectories was established. Finally, an integer optimization technique was employed to solve the optimal flight sequence for multiple reusable vehicles undertaking repeated round-trips.