When a spacecraft lands, a large shock load can lead to undesirable responses such as rebound and tripping. The authors previously discussed the problem of controlling these shock responses using momentum exchange impact dampers (MEIDs). MEIDs are classified by momentum exchange directions as follows: Upper-MEID (U-MEID) that launches the damper mass upward, Lower-MEID (L-MEID) that drops the damper mass downward, and Generalized-MEID (G-MEID) consisting of U-MEID and L-MEID, and G-MEID-A (G-MEID-Advanced) that has both upward and downward launching effect on single damper mass, by introducing initial tension to the MEID spring. However, studies of these MEIDs are mainly based on one-dimensional motion. Two-dimensional motion analyses have been done for only U-MEID. This research aims to derive the generalized MEID design methodology for two-dimensional motions. G-MEID-A, that is the most effective one for shock response control in previous MEIDs in the one-dimensional motion, are applied to multi-legged landing gear system. There are two damper masses, one is released to control spacecraft attitude, and the other is released to reduce landing shock. Their parameter design and optimal release timing are discussed in this paper. The effectiveness and robustness against landing slope angle variation of the proposed design methodology are verified by simulations.