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 ($Delta dsim10~kpc$) 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.
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