  Neutron $^3P_2$ superfluids consisting of neutron pairs with the total
angular momentum $J=2$ with spin-triplet and $P$-wave are believed to be
realized in neutron star cores. Within the Ginzburg-Landau theory it was
previously found that a singly quantized vortex is split into two
half-quantized non-Abelian vortices connected by one (or three) soliton(s)
forming a vortex molecule with the soliton bond(s), in the absence (presence)
of magnetic field parallel to them. In this paper, we investigate proximity
effects of two vortex molecules by exhausting all possible two vortex molecule
states consisting of four half-quantized vortices and determining the phase
diagram spanned by the magnetic field and rotation speed. As the rotation speed
is increased, the distance between the two vortex molecules becomes shorter. In
the magnetic field below the critical value, we find that as the rotation speed
is increased, the two separated vortex molecules transit to a dimerized vortex
molecule, where the two vortex molecules are bridged by two solitons that we
call "covalent bonds" in analogy with chemical molecules. We also find that the
orders of the constituent half-quantized vortex cores transit from a
ferromagnetic order to a cyclic order as the vortex molecules come closer. On
the other hand, no dimerization occurs in the magnetic field above the critical
value. Instead, we find a transition for the polarization direction of the
vortex molecules from a configuration parallel to the separation to one
perpendicular to the separation as they come closer. We also show some examples
of three and four vortex molecule states.
