We present a study of molecular gas, traced via CO (3-2) from Atacama Large Millimeter/submillimeter Array data, of four z < 0.2, 'radio quiet', type 2 quasars (L-bol similar to 10(45.3)-10(46.2) erg s(-1); L1.4GHz similar to 1023.7-1024.3 W Hz(-1)). Targets were selected to have extended radio lobes (>= 10 kpc), and compact, moderate-power jets (1-10 kpc; P-jet similar to 10(43.2)-10(43.7) erg s(-1)). All targets show evidence of central molecular outflows, or injected turbulence, within the gas discs (traced via high-velocity wing components in CO emission-line profiles). The inferred velocities (V-out = 250-440 km s(-1)) and spatial scales (0.6-1.6 kpc), are consistent with those of other samples of luminous low-redshift active galactic nuclei. In two targets, we observe extended molecular gas structures beyond the central discs, containing 9-53 per cent of the total molecular gas mass. These structures tend to be elongated, extending from the core, and wrap-around (or along) the radio lobes. Their properties are similar to the molecular gas filaments observed around radio lobes of, mostly 'radio loud', brightest cluster galaxies. They have the following: projected distances of 5-13 kpc; bulk velocities of 100-340 km s(-1); velocity dispersion of 30-130 km s(-1); inferred mass outflow rates of 4-20 M-circle dot yr(-1); and estimated kinetic powers of 10(40.3)-10(41.7) erg s(-1). Our observations are consistent with simulations that suggest moderate-power jets can have a direct (but modest) impact on molecular gas on small scales, through direct jet-cloud interactions. Then, on larger scales, jet-cocoons can push gas aside. Both processes could contribute to the long-term regulation of star formation.