We present deep emission-line imaging taken with the new SOAR Optical Imager of the brightest cluster galaxy (BCG) in the nearby (z = 0.035) X-ray cluster of galaxies 2A0335+096. We also present our analysis of additional, multiwavelength observations for the BCG, including long-slit optical spectroscopy, archival VLA radio data, Chandra X-ray imaging, and XMM-Newton UV imaging. Cluster 2A0335+096 is a bright, cool-core X-ray cluster, once known as a cooling flow. Within the highly disturbed core revealed by Chandra X-ray observations, 2A0335+096 hosts a luminous and highly structured optical emission-line system, spanning the BCG and its companion. We confirm that the redshift of the companion is within 100 km s^-1 of the BCG, has certainly interacted with it, and is likely bound to it. The comparison of optical and radio images shows curved filaments in Hα emission surrounding the newly resolved radio source. The velocity structure of the emission-line bar between the BCG nucleus and the companion galaxy provides strong evidence for an interaction between the BCG and its northeast companion in the last ~50 million years. The age of the radio source is similar to the interaction time, so this interaction may have provoked an episode of radio activity. We estimate a star formation rate of 7 M yr^-1 from the Hα and archival UV data. This rate is similar to, but somewhat lower than, the revised X-ray cooling rate of 10-30 M yr^-1 in the vicinity of the BCG, estimated from XMM-Newton spectra by Peterson and coworkers. The Hα nebula is limited to a region of high X-ray surface brightness and cool X-ray temperatures. However, the detailed structures of Hα and X-ray gas differ. The peak of the X-ray surface brightness is not the peak of Hα emission, nor does it lie in the BCG. The estimated age of the radio lobes and their interaction with the optical emission-line gas, the estimated timescale for depletion and accumulation of cold gas, and the dynamical time in the system are all similar, suggesting a common trigger mechanism.