  We study the dynamics of phase defects trapped in a finite optically
imprinted ring lattice in binary polariton condensates, under the influence of
the cross-interaction (CI) between the condensates in different spin components
and the spin-orbit interaction (SOI). In this configuration, we find that a
vortex circulates unidirectionally in optically induced orbits because of the
Magnus force acting in the polariton fluid, and the vortex' angular velocity is
influenced by the SOI and CI. Interestingly, in our system, these two
interactions can also lead to elongated and frozen phase defects, forming a
frozen dark solution with similarity to a dark soliton but with finite size in
both spin components. When the dark solution is stretched further to occupy the
entire orbit of a condensate ring, the phase defect triggers a snake
instability and induces the decay of the dark ring solution. The circulation
direction of a single vortex is determined by the Magnus force. This situation
is more complex for the group motion of multiple vortices because of
significant vortex-antivortex interaction. The collective motion of such vortex
constellations, however, can be determined by the SOI.
