  Golovich et al. 2017b presents an optical imaging and spectroscopic survey of
29 radio relic merging galaxy clusters. In this paper, we study this survey to
identify substructure and quantify the dynamics of the mergers. Using a
combined photometric and spectroscopic approach, we identify the minimum number
of substructures in each system to describe the galaxy populations and estimate
the line of sight velocity difference between likely merging subclusters. We
find that the line-of-sight velocity components of the mergers are typically
small compared with the maximum three dimensional relative velocity (usually
$<1000$ km s$^{-1}$ and often consistent with zero). This suggests that the
merger axes of these systems are generally in or near the plane of the sky
matching findings in magneto-hydrodynamical simulations. In 28 of the 29
systems we identify substructures in the galaxy population aligned with the
radio relic(s) and presumed associated merger induced shock. From this
ensemble, we identify eight systems to include in a `gold' sample that is prime
for further observation, modeling, and simulation study. Additional papers will
present weak lensing mass maps and dynamical modeling for each merging system,
ultimately leading to new insight into a wide range of astrophysical phenomena
at some of the largest scales in the universe.
