We present the first results of an MMT/Hectospec campaign to measure the kinematics of globular clusters (GCs) around M49 - the brightest galaxy in the Virgo galaxy cluster, which dominates the Virgo B subcluster. The data include kinematic tracers beyond 95 kpc (∼5.2 effective radii) for M49 for the first time, enabling us to achieve three key insights reported here. First, beyond ∼20′-30′ (∼100-150 kpc), the GC kinematics sampled along the minor photometric axis of M49 become increasingly hotter, indicating a transition from GCs related to M49 to those representing the Virgo B intra-cluster medium. Second, there is an anomaly in the line-of-sight radial velocity dispersion (σ r,los) profile in an annulus ∼10-15′ (∼50-90 kpc) from M49 in which the kinematics cool by Δσ r,los ≈ 150 km s-1 relative to those in- or outward. The kinematic fingerprint of a previous accretion event is hinted at in projected phase-space, and we isolate GCs that both give rise to this feature, and are spatially co-located with two prominent stellar shells in the halo of M49. Third, we find a subsample of GCs with velocities representative of the dwarf galaxy VCC 1249 that is currently interacting with M49. The spatial distribution of these GCs closely resembles the morphology of VCC 1249's isophotes, indicating that several of these GCs are likely in the act of being stripped from the dwarf during its passage through M49's halo. Taken together, these results point toward the opportunity of witnessing ongoing giant halo assembly in the depths of a cluster environment.