  Cluster galaxies are subject to the ram pressure exerted by the intracluster
medium, which can perturb or even strip away their gas while leaving the stars
undisturbed. We model the distribution and kinematics of the stars and the
molecular gas in four late-type cluster galaxies (JO201, JO204, JO206, and
JW100), which show tails of atomic and ionized gas indicative of ongoing ram
pressure stripping. We analyze MUSE@VLT data and CO data from ALMA searching
for signatures of radial gas flows, ram pressure stripping, and other
perturbations. We find that all galaxies, with the possible exception of JW100,
host stellar bars. Signatures of ram pressure are found in JO201 and JO206,
which also shows clear indications of ongoing stripping in the molecular disk
outskirts. The stripping affects the whole molecular gas disk of JW100. The
molecular gas kinematics in JO204 is instead dominated by rotation rather than
ram pressure. We also find indications of enhanced turbulence of the molecular
gas compared to field galaxies. Large-scale radial flows of molecular gas are
present in JO204 and JW100, but more uncertain in JO201 and JO206. We show that
our sample follows the molecular gas mass-size relation, confirming that it is
essentially independent of environment even for the most extreme cases of
stripping. Our findings are consistent with the molecular gas being affected by
the ram pressure on different timescales and less severely than the atomic and
ionized gas phases, likely because the molecular gas is denser and more
gravitationally bound to the galaxy.
