Amplitude models are applied to studies of resonance structure in D-0 -> (KSK-)-K-0 pi(+) and D-0 -> (KSK+)-K-0 pi(-) 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/c(2) around the K*(892)(+/-) resonance. Two formulations for the K pi S-wave are used, both of which give a good description of the data. The ratio of branching fractions B(D-0 -> (KSK+)-K-0 pi(-))/B(D-0 -> (KSK-)-K-0 pi(+)) 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.