Querying the Spitzer archive for optically-selected active galactic nuclei (AGN) observed in high-resolution-mode spectroscopy, we identified radio and/or interacting galaxies with highly turbulent motions of H 2 gas at a temperature of a few hundred Kelvin. Unlike all other AGN that have unresolved H 2 line profiles at a spectral resolution of ∼600, 3C 236, 3C 293, IRAS 09039+0503, MCG-2-58-22 and Mrk 463E have intrinsic velocity dispersions exceeding 200 km s −1 for at least two of the rotational S0, S1, S2, and S3 lines. In a sixth source, 4C 12.50, a blue wing was detected in the S1 and S2 line profiles, indicating the presence of a warm molecular gas component moving at −640 km s −1 with respect to the bulk of the gas at systemic velocity. Its mass is 5.2 × 10 7 M , accounting for more than one fourth of the H 2 gas at 374 K, but less than 1% of the cold H 2 gas computed from CO observations. Because no diffuse gas component of 4C 12.50 has been observed to date to be moving at more than 250 km s −1 from systemic velocity, the H 2 line wings are unlikely to be tracing gas in shock regions along the tidal tails of this merging system. They can instead be tracing gas driven by a jet or entrained by a nuclear outflow, which is known to emerge from the west nucleus of 4C 12.50. It is improbable that such an outflow, with an estimated mass loss rate of 130 M yr −1 , entirely quenches the star formation around this nucleus.