  We present detailed studies of a $z=2.12$ submillimeter galaxy, ALESS67.1,
using sub-arcsecond resolution ALMA, AO-aided VLT/SINFONI, and HST/CANDELS data
to investigate the kinematics and spatial distributions of dust emission (870
$\mu$m continuum), $^{12}$CO($J$=3-2), strong optical emission lines, and
visible stars. Dynamical modelling of the optical emission lines suggests that
ALESS67.1 is not a pure rotating disk but a merger, consistent with the
apparent tidal features revealed in the HST imaging. Our sub-arcsecond
resolution dataset allow us to measure half-light radii for all the tracers,
and we find a factor of 4-6 smaller sizes in dust continuum compared to all the
other tracers, including $^{12}$CO, and UV and H$\alpha$ emission is
significantly offset from the dust continuum. The spatial mismatch between UV
continuum and the cold dust and gas reservoir supports the explanation that
geometrical effects are responsible for the offset of dusty galaxy on the
IRX-$\beta$ diagram. Using a dynamical method we derive an $\alpha_{\rm
CO}=1.8\pm1.0$, consistent with other SMGs that also have resolved CO and dust
measurements. Assuming a single $\alpha_{\rm CO}$ value we also derive resolved
gas and star-formation rate surface densities, and find that the core region of
the galaxy ($\lesssim5$ kpc) follows the trend of mergers on the
Schmidt-Kennicutt relationship, whereas the outskirts ($\gtrsim5$ kpc) lie on
the locus of normal star-forming galaxies, suggesting different star-formation
efficiencies within one galaxy. Our results caution against using single size
or morphology for different tracers of the star-formation activity and gas
content of galaxies, and therefore argue the need to use spatially-resolved,
multi-wavelength observations to interpret the properties of SMGs, and perhaps
even for $z>1$ galaxies in general.
