Most successful galaxy formation scenarios now postulate that the intense star formation in massive, high-redshift galaxies during their major growth period was truncated when powerful AGNs launched galaxy-wide outflows of gas that removed large parts of the interstellar medium. The most powerful radio galaxies at z~2 show clear signatures of such winds, but are too rare to be good representatives of a generic phase in the evolution of all massive galaxies at high redshift. Here we present SINFONI imaging spectroscopy of 12 radio galaxies at z~2 that are intermediate between the most powerful radio and vigorous starburst galaxies in radio power, and common enough to represent a generic phase in the early evolution of massive galaxies. The kinematic properties are diverse, with regular velocity gradients with amplitudes of Delta v=200-400 km s^-1 as in rotating disks as well as irregular kinematics with multiple velocity jumps of a few 100 km s^-1. Line widths are generally high, typically around FWHM=800 km s^-1, consistent with wind velocities in hydrodynamic models. A broad H-alpha line in one target implies a black hole mass of a few 10^9 M$_sun. The ratio of line widths, sigma, to bulk velocity, v, is so large that even the gas in galaxies with regular velocity fields is unlikely to be gravitationally bound. It is unclear, however, whether the large line widths are due to turbulence or unresolved, local outflows as are sometimes observed at low redshifts. Comparison of the kinetic energy with the energy supply from the AGN through jet and radiation pressure suggests that the radio source still plays a dominant role for feedback, consistent with low-redshift radio-loud quasars.