We present new, deep near-infrared SINFONI @ VLT integral field spectroscopy of the gas cloud G2 in the Galactic Center, from late 2013 August, 2014 April, and 2014 July. G2 is visible in recombination line emission. The spatially resolved kinematic data track the ongoing tidal disruption. The cloud reached minimum distance to the MBH of 1950 Schwarzschild radii. As expected for an observation near the pericenter passage, roughly half of the gas in 2014 is found at the redshifted, pre-pericenter side of the orbit, while the other half is at the post-pericenter, blueshifted side. We also present an orbital solution for the gas cloud G1, which was discovered a decade ago in L'-band images when it was spatially almost coincident with Sgr A*. The orientation of the G1 orbit in the three angles is almost identical to that of G2, but it has a lower eccentricity and smaller semi-major axis. We show that the observed astrometric positions and radial velocities of G1 are compatible with the G2 orbit, assuming that (1) G1 was originally on the G2 orbit preceding G2 by 13 yr, and (2) a simple drag force acted on it during pericenter passage. Taken together with the previously described tail of G2, which we detect in recombination line emission and thermal broadband emission, we propose that G2 may be a bright knot in a much more extensive gas streamer. This matches purely gaseous models for G2, such as a stellar wind clump or the tidal debris from a partial disruption of a star.