  We study the vortex formation in coupled atomic and molecular condensates in
a rotating double well trap by numerically solving the coupled Gross-Pitaevskii
like equations. Starting with the atomic condensate in the double well
potential we considered two-photon Raman photoassociation for coherent
conversion of atoms to molecules. It is shown that the competition between
atom-molecule coupling strength and repulsive atom-molecule interaction
controls the spacings between atomic and molecular vortices and the rotation
frequency of the trap is the key player for controlling the number of visible
atomic and molecular vortices. Whereas the Raman detuning controls the spacing
between atomic and molecular vortices as well as the number of atomic and
molecular vortices in the trap. We have shown by considering the molecular
lattices the distance between two molecular vortices can be controlled by
varying the Raman detuning. In addition we have found that the Feynman rule
relating the total number of vortices and average angular momentum both for
atoms and molecules can be satisfied by considering the atomic and molecular
vortices those are hidden in density distribution and seen as singularities in
phase distribution of the coupled system except for the lattice structure where
molecular vortices are overlapped with each other. It is found that although
the number of visible/core vortices in atomic and molecular vortex lattices
depends significantly on the system parameters the number of atomic and
molecular hidden vortices remains constant in most of the cases.
