Amplitude models are applied to studies of resonance structure in D 0 → K 0 S K − π + and D 0 → K 0 S K + π − decays using p p collision data corresponding to an integrated luminosity of 3.0     fb − 1 collected by the LHCb experiment. Relative magnitude and phase information is determined, and coherence factors and related observables are computed for both the whole phase space and a restricted region of 100     MeV / c 2 around the K ∗ ( 892 ) ± resonance. Two formulations for the K π   S -wave are used, both of which give a good description of the data. The ratio of branching fractions B ( D 0 → K 0 S K + π − ) / B ( D 0 → K 0 S K − π + ) is measured to be 0.655 ± 0.004 ( stat ) ± 0.006 ( syst ) over the full phase space and 0.370 ± 0.003 ( stat ) ± 0.012 ( syst ) in the restricted region. A search for C P violation is performed using the amplitude models and no significant effect is found. Predictions from SU(3) flavor symmetry for K ∗ ( 892 ) K amplitudes of different charges are compared with the amplitude model results.