Amplitude models are applied to studies of resonance structure in D0→K0SK−π+ and D0→K0SK+π− decays using pp 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/c2 around the K∗(892)± resonance. Two formulations for the Kπ S-wave are used, both of which give a good description of the data. The ratio of branching fractions B(D0→K0SK+π−)/B(D0→K0SK−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 CP 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.