  Discoveries of low mass galaxy pairs and groups are increasing. Studies
indicate that dwarf galaxy pairs are gas rich in the field and exhibit elevated
star formation rates, suggestive of interactions. Lacking are dynamical models
of observed dwarf galaxy pairs to disentangle the physical processes regulating
their baryon cycles. We present new optical data and the first detailed
theoretical model of an observed tidal encounter between two isolated low mass
galaxies, NGC 4490 & NGC 4485. This system is an isolated analog of the
Magellanic Clouds and is surrounded by a ~50 kpc extended HI envelope. We use
hybrid $N$-body and test-particle simulations along with a visualization
interface $Identikit$ to simultaneously reproduce the observed present-day
morphology and kinematics. Our results demonstrate how repeated encounters
between two dwarf galaxies can "park" baryons at very large distances, without
the aid of environmental effects. Our best match to the data is an 8:1 mass
ratio encounter where a one-armed spiral is induced in the NGC 4490-analog,
which we postulate explains the nature of diffuse starlight presented in the
new optical data. We predict that the pair will fully merge in ~370 Myr, but
that the extended tidal features will continue to evolve and return to the
merged remnant over ~5 Gyr. This pre-processing of baryons will affect the
efficiency of gas stripping if such dwarf pairs are accreted by a massive host.
In contrast, in isolated environments this study demonstrates how dwarf-dwarf
interactions can create a long-lived supply of gas to the merger remnant.
