  We present Magellan/IMACS, Anglo-Australian Telescope/AAOmega+2dF, and Very
Large Telescope/GIRAFFE+FLAMES spectroscopy of the CarinaII (Car II) & Carina
III (Car III) dwarf galaxy candidates, recently discovered in the Magellanic
Satellites Survey (MagLiteS). We identify 18 member stars in Car II, including
2 binaries with variable radial velocities and 2 RR Lyrae stars. The other 14
members have a mean heliocentric velocity $v_{\rm hel} = 477.2 \pm 1.2$ km/s
and a velocity dispersion of $\sigma_v = 3.4^{+1.2}_{-0.8}$ km/s. Assuming Car
II is in dynamical equilibrium, we derive a total mass within the half-light
radius of $1.0^{+0.8}_{-0.4} \times 10^{6} M_\odot$, indicating a mass-to-light
ratio of $369^{+309}_{-161} M_\odot/L_\odot$. From equivalent width
measurements of the calcium triplet lines of 9 RGB stars, we derive a mean
metallicity of [Fe/H] = $-2.44 \pm 0.09$ with dispersion $\sigma_{\rm [Fe/H]} =
0.22 ^{+0.10}_{-0.07}$. Considering both the kinematic and chemical properties,
we conclude that Car II is a dark-matter-dominated dwarf galaxy. For Car III,
we identify 4 member stars, from which we calculate a systemic velocity of
$v_{\rm hel} = 284.6^{+3.4}_{-3.1}$ km/s. The brightest RGB member of Car III
has a metallicity of [Fe/H] $= -1.97 \pm 0.12$. Due to the small size of the
Car III spectroscopic sample, we cannot conclusively determine its nature.
Although these two systems have the smallest known physical separation ($\Delta
d\sim10~kpc$) among Local Group satellites, the large difference in their
systemic velocities, $\sim200$ km/s, indicates that they are unlikely to be a
bound pair. One or both systems are likely associated with the Large Magellanic
Cloud (LMC), and may remain LMC satellites today. No statistically significant
excess of $\gamma$-rays emission is found at the locations of Car II and Car
III in eight years of Fermi-LAT data.
