  Context. Spatially resolved observations of the ionized and molecular gas are
critical for understanding the physical processes that govern the interstellar
medium (ISM) in galaxies. Aims. To study the morpho-kinematic properties of the
ionized and molecular gas in three dusty starburst galaxies at $z = 0.12-0.17$
to explore the relation between molecular ISM gas phase dynamics and the
star-formation activity. Methods. We analyse $\sim$kpc-scale ALMA CO(1--0) and
seeing limited SINFONI Paschen-$\alpha$ observations. We use a dynamical mass
model, which accounts for beam-smearing effects, to constrain the CO-to-H$_2$
conversion factor. Results. One starburst galaxy shows irregular morphology
which may indicate a major merger, while the other two systems show disc-like
morpho-kinematics. The two disc-like starbursts show molecular gas velocity
dispersion values comparable with that seen in local LIRG/ULIRGs, but in an ISM
with molecular gas fraction and surface density values consistent to that
reported for local star-forming galaxies. These molecular gas velocity
dispersion values can be explained by assuming vertical pressure equilibrium.
The star-formation activity is correlated with the molecular gas content
suggesting depletion times of the order of $\sim 0.1-1$ Gyr. The star formation
rate surface density ($\Sigma_{\rm SFR}$) correlates with the ISM pressure set
by self-gravity ($P_{\rm grav}$) following a power law with an exponent close
to 0.8. Conclusions. In dusty disc-like starburst galaxies, our data support
the scenario in which the molecular gas velocity dispersion values are driven
by the ISM pressure set by self-gravity, responsible to maintain the vertical
pressure balance. The correlation between $\Sigma_{\rm SFR}$ and $P_{\rm grav}$
suggests that, in these dusty starbursts galaxies, the star formation activity
arises as a consequence of the ISM pressure balance.
