We extend results first announced by Franz et al., that identified vA351=H346 in the Hyades as a multiple star system containing a white dwarf. With Hubble Space Telescope Fine Guidance Sensor fringe tracking and scanning, and more recent speckle observations, all spanning 20.7years, we establish a parallax, relative orbit, and mass fraction for two components, with a period, P=2.70yr and total mass 2.1M{sun}. With ground-based radial velocities from the McDonald Observatory Otto Struve 2.1m Telescope Sandiford Spectrograph, and Center for Astrophysics Digital Speedometers, spanning 37 years, we find that component B consists of BC, two M-dwarf stars orbiting with a very short period (P_BC_=0.749days), having a mass ratio M_C_/M_B_=0.95. We confirm that the total mass of the system can only be reconciled with the distance and component photometry by including a fainter, higher-mass component. The quadruple system consists of three M dwarfs (A, B, C) and one white dwarf (D). We determine individual M-dwarf masses M_A_=0.53{+/-}0.10M{sun}, M_B_=0.43{+/-}0.04M{sun}, and M_C_=0.41{+/-}0.04M{sun}. The white dwarf mass, 0.54{+/-}0.04M{sun}, comes from cooling models, an assumed Hyades age of 670Myr, and consistency with all previous and derived astrometric, photometric, and radial velocity results. Velocities from H{alpha} and HeI emission lines confirm the BC period derived from absorption lines, with similar (HeI) and higher (H{alpha}) velocity amplitudes. We ascribe the larger H{alpha} amplitude to emission from a region each component shadows from the other, depending on the line of sight.