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We present Hubble Space Telescope WFC3 F160W imaging and infrared spectral energy distributions for 12 extremely luminous, obscured active galactic nuclei (AGNs) at 1.8 < z < 2.7 selected via “hot, dust-obscured” mid-infrared colors. Their infrared luminosities span (2–15) × 1013L⊙, making them among the most luminous objects in the universe at z ∼ 2. In all cases, the infrared emission is consistent with arising at least for the most part from AGN activity. The AGN fractional luminosities are higher than those in either submillimeter galaxies or AGNs selected via other mid-infrared criteria. Adopting the G, M20, and A morphological parameters, together with traditional classification boundaries, infers that three-quarters of the sample are mergers. Our sample does not, however, show any correlation between the considered morphological parameters and either infrared luminosity or AGN fractional luminosity. Moreover, the asymmetries and effective radii of our sample are distributed identically to those of massive galaxies at z ∼ 2. We conclude that our sample is not preferentially associated with mergers, though a significant merger fraction is still plausible. Instead, we propose that our sample includes examples of the massive galaxy population at z ∼ 2 that harbor a briefly luminous, “flickering” AGN and in which the G and M20 values have been perturbed due to either the AGN and/or the earliest formation stages of a bulge in an inside-out manner. Furthermore, we find that the mass assembly of the central black holes in our sample leads the mass assembly of any bulge component. Finally, we speculate that our sample represents a small fraction of the immediate antecedents of compact star-forming galaxies at z ∼ 2. [ABSTRACT FROM AUTHOR]