We present a study of molecular gas, traced via CO (3–2) from ALMA data, of four z<0.2, ‘radio quiet’, type 2 quasars (Lbol ∼ 1045.3 − 46.2 erg s−1; L1.4 GHz ∼ 1023.7 − 24.3 W Hz−1). Targets were selected to have extended radio lobes (≥ 10 kpc), and compact, moderate-power jets (1–10 kpc; Pjet ∼ 1043.2 − 43.7 erg s−1). All targets show evidence of central molecular outflows, or injected turbulence, within the gas disks (traced via high-velocity wing components in CO emission-line profiles). The inferred velocities (Vout=250 – 440 km s−1) and spatial scales (0.6 – 1.6 kpc), are consistent with those of other samples of luminous low-redshift AGN. In two targets, we observe extended molecular gas structures beyond the central disks, containing 9 – 53 % 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: 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⊙ yr−1; and estimated kinetic powers of 1040.3 − 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.