  Using hydrodynamical $N$-body simulations, we show that the observed
structure and kinematics of the extremely metal-poor, dwarf irregular galaxy
DDO 68 is compatible with a merger event with at least two smaller satellite
galaxies. We were able to obtain a self-consistent model that simultaneously
reproduces several of its observed features, including: the very asymmetric and
disturbed shape of the stellar component, the overall HI distribution and its
velocity field, the arc-like stellar structure to the west, the low-surface
brightness stellar stream to the north. The model implies the interaction of
the main progenitor of DDO 68 with two systems with dynamical masses
$7\times10^8\,M_{\odot}$ and almost $10^8\,M_{\odot}$ -- 1/20 and 1/150 times
the dynamical mass of DDO 68, respectively. We show that the merger between DDO
68 and the most massive of its satellites offers a route to explain the large
offset of DDO 68 from the mass-metallicity relation. Assuming that the
interacting galaxies have metallicities prior to the merger compatible with
those of galaxies with similar stellar masses, we provide quantitative evidence
that gas mixing alone does not suffice at diluting the gas of the two
components; according to our simulations, the HII regions observed along the
Cometary Tail trace the low metallicity of the accreted satellite rather than
that of DDO 68's main body. In this case, the mass corresponding to the low
metallicity is that of the secondary body and DDO 68 becomes consistent with
the mass-metallicity relation.
