We investigate the evolution of the interstellar medium (ISM) in self-consistent, chemodynamical simulations of the Magellanic Clouds (MCs) during their recent (z <0.3) past. An explicit modelling of dust and molecular hydrogen lifecycles enables us to compare our models against the observed properties of the ISM, including elemental depletion from the gas-phase. Combining this model with a tidal-dominated paradigm for the formation for the Magellanic Stream and Bridge, we reproduce the age-metallicity relations, long gas depletion time-scales, and presently observed dust and molecular hydrogen masses of the MCs to within their respective uncertainties. We find that these models' enrichment depends sensitively on the processing of dust within the ISM and the dynamical influence of external tides/stellar bars. The ratio of characteristic dust destruction time-scales in our Small Magellanic Cloud (SMC) and Large Magellanic Cloud (LMC) models, a governing parameter of our models' evolution, is consistent with estimates based on observed supernova (SN) rates. Our reference MC models tend to exhibit the disputed universal dust-to-metal ratio, which we argue stems from the adoption of high SNe II condensation efficiencies. Our models are the first to reproduce the one-tenth solar metallicity of the Stream/Leading Arm following tidal stripping of the SMC the hypothesis that the LMC contributes a metal-rich filament to the Stream, as implied by recent kinematic and abundance analyses, is also appraised in this study. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.