We present high-resolution ALMA Band 6 and 7 observations of the tidally disrupted protoplanetary disks of the RW Aurigae binary. Our observations reveal tidal streams in addition to the previously observed tidal arm around RW Aur A. The observed configuration of tidal streams surrounding RW Aur A and B is incompatible with a single star–disk tidal encounter, suggesting that the RW Aurigae system has undergone multiple flyby interactions. We also resolve the circumstellar disks around RW Aur A and B, with CO radii of 58 au and 38 au consistent with tidal truncation, and 2.5 times smaller dust emission radii. The disks appear misaligned by 12° or 57°. Using new photometric observations from the American Association of Variable Star Observers (AAVSO) and the All Sky Automated Survey for SuperNovae (ASAS-SN) archives, we have also identified an additional dimming event of the primary that began in late 2017 and is currently ongoing. With over a century of photometric observations, we are beginning to explore the same spatial scales as ALMA.