Context : Ionized outflows are ubiquitous in non-radio-loud obscured quasars ( QSO2s ) at different redshifts . However , the actual size of the outflows and their efficiency for gas ejection and star formation truncation are controversial . Large-scale ( exceeding several kiloparsec ) extended radio structures might be necessary to identify ( even to trigger ) outflow signatures across such large spatial scales . Aims : We search for large-scale ionized outflows associated with six optically selected QSO2 ( five non-radio-loud and one radio-loud ) at z \sim 0.2–0.5 , targeting objects with extended radio structures . We also investigate the dynamical state of the QSO2 host galaxies . Methods : We obtained data with the optical imager and long-slit spectrograph ( OSIRIS ) mounted on the 10.4m Gran Telescopio Canarias Spanish telescope ( GTC ) for these six QSO2 with the slit located along the radio axis . We traced the gas kinematics with the [ OIII ] \lambda 4959,5007 lines to investigate ionized outflows and characterize the dynamical state of the host galaxies . This second study was complemented with previously published spectroscopic data obtained with the multimode focal reducer and low dispersion spectrograph ( FORS2 ) mounted on the Very Large Telescope ( VLT ) of 13 more QSO2 at similar z . Results : We identify ionized outflows in four out of the six QSO2 observed with the GTC . The outflows are spatially unresolved in two QSO2 and compact in a third ( radial size of R = 0.8 \pm 0.3 kpc ) . Of particular interest is the radio-quiet QSO2 SDSS 0741+3020 at z = 0.47 . It is associated with a giant \sim 112 kpc nebula . An ionized outflow probably induced by the radio structures has been detected along the axis defined by the central \sim 1″ radio structure , extending up to at least \sim 4 kpc from the active galactic nucleus ( AGN ) . Turbulent gas ( \sigma \sim 130 km s ^ { -1 } ) has also been detected across the giant gas nebula up to \sim 40 kpc from the AGN . This turbulence may have been induced by outflows triggered by the interaction between a so-far undetected large-scale radio source and the nebula . Regarding the dynamical state of the host galaxies , we find that the majority of the QSO2 show v/ \sigma < 1 , implying that they are dominated by random motions ( so-called dispersion-dominated systems ) . Most ( 17 of 19 ) fall in the area of the E/S0 galaxies in the dynamical diagram v/ \sigma versus \sigma . None are consistent with spiral or disk galaxies . Conclusions :