  We present a study of the stellar host galaxy, CO (1$-$0) molecular gas
distribution and AGN emission on 50 to 500 pc-scales of the gravitationally
lensed dust-obscured AGN MG J0751+2716 and JVAS B1938+666 at redshifts 3.200
and 2.059, respectively. By correcting for the lensing distortion using a
grid-based lens modelling technique, we spatially locate the different emitting
regions in the source plane for the first time. Both AGN host galaxies have 300
to 500 pc-scale size and surface brightness consistent with a
bulge/pseudo-bulge, and 2 kpc-scale AGN radio jets that are embedded in
extended molecular gas reservoirs that are 5 to 20 kpc in size. The CO (1$-$0)
velocity fields show structures possibly associated with discs (elongated
velocity gradients) and interacting objects (off-axis velocity components).
There is evidence for a decrement in the CO (1$-$0) surface brightness at the
location of the host galaxy, which may indicate radiative feedback from the
AGN, or offset star formation.We find CO-H$_2$ conversion factors of around
$\alpha_{\rm CO} = 1.5\pm0.5$ (K km s$^{-1}$ pc$^2$)$^{-1}$, molecular gas
masses of $> 3\times10^{10}$ M$_{\odot}$, dynamical masses of $\sim 10^{11}$
M$_{\odot}$ and gas fractions of around 60 per cent. The intrinsic CO line
luminosities are comparable to those of unobscured AGN and dusty star-forming
galaxies at similar redshifts, but the infrared luminosities are lower,
suggesting that the targets are less efficient at forming stars. Therefore,
they may belong to the AGN feedback phase predicted by galaxy formation models,
because they are not efficiently forming stars considering their large amount
of molecular gas.
