There is X-ray, optical, and mid-infrared imaging and spectroscopic evidence that the late-stage ultraluminous infrared galaxy merger Mrk 273 hosts a powerful active galactic nucleus (AGN). However, the exact location of the AGN and the nature of the nuclei have been difficult to determine due to dust obscuration and the limited wavelength coverage of available high-resolution data. Here we present near-infrared integral-field spectra and images of the nuclear region of Mrk 273 taken with OSIRIS and NIRC2 on the Keck II Telescope with laser guide star adaptive optics. We observe three spatially resolved components, and analyze the local molecular and ionized gas emission lines and their kinematics. We confirm the presence of the hard X-ray AGN in the southwest nucleus. In the north nucleus, we find a strongly rotating gas disk whose kinematics indicate a central black hole of mass 1.04 +/- 0.1 x 10^9 Msun. The H2 emission line shows an increase in velocity dispersion along the minor axis in both directions, and an increased flux with negative velocities in the southeast direction; this provides direct evidence for a collimated molecular outflow along the axis of rotation of the disk. The third spatially distinct component appears to the southeast, 640 and 750 pc from the north and southwest nuclei, respectively. This component is faint in continuum emission but shows several strong emission line features, including [Si vi] 1.964 {mu}m which traces an extended coronal-line region. The geometry of the [Si vi] emission combined with shock models and energy arguments suggest that [Si vi] in the southeast component must be at least partly ionized by the SW AGN or a putative AGN in the northern disk, either through photoionization or through shock-heating from strong AGN- and circumnuclear starburst-driven outflows. This lends support to a scenario in which Mrk 273 may be a dual AGN system.