We study the dynamics of faint stellar substructures around the Umbrella Galaxy, NGC 4651, which hosts a dramatic system of streams and shells formed through the tidal disruption of a nucleated dwarf elliptical galaxy. We elucidate the basic characteristics of the system (colours, luminosities, stellar masses) using multiband Subaru/Suprime-Cam images. The implied stellar mass ratio of the ongoing merger event is ~1:50. We identify candidate kinematic tracers (globular clusters, planetary nebulae, HII regions) and follow up a subset with Keck/DEIMOS (DEep Imaging Multi-object Spectrograph) spectroscopy to obtain velocities. We find that 15 of the tracers are likely associated with halo substructures, including the probable stream progenitor nucleus. These objects delineate a kinematically cold feature in position-velocity phase space. We model the stream using single test particle orbits, plus a rescaled pre-existing N-body simulation. We infer a very eccentric orbit with a period of ~0.35Gyr and turning points at ~2-4 and ~40kpc, implying a recent passage of the satellite through the disc, which may have provoked the visible disturbances in the host galaxy. This work confirms that the kinematics of low surface brightness substructures can be recovered and modelled using discrete tracers - a breakthrough that opens up a fresh avenue for unravelling the detailed physics of minor merging.