  We develop and implement a model to analyze the internal kinematics of galaxy
clusters that may contain subpopulations of galaxies that do not independently
trace the cluster potential. The model allows for substructures within the
cluster environment, disentangles cluster members from contaminating foreground
and background galaxies, and includes an overall cluster rotation term as part
of the cluster kinematics. We estimate the cluster velocity dispersion and/or
mass while marginalizing over uncertainties in all of the above complexities.
In a first application to our published data for Abell 267 (A267), we find no
evidence for cluster rotation but we identify up to five distinct galaxy
subpopulations. We use these results to explore the sensitivity of inferred
cluster properties to the treatment of substructure. Compared to a model that
assumes no substructure, our substructure model reduces the dynamical mass of
A267 by $\sim 20\%$ and shifts the cluster mean velocity by $\sim 100$ km
s$^{-1}$, approximately doubling the offset with respect to the velocity of
A267's brightest cluster galaxy. Embedding the spherical Jeans equation within
this framework, we infer for A267 a dark matter halo of mass
$M_{200}=6.77\pm1.06\times10^{14}M_\odot/h$, concentration
$\log_{10}c_{200}=0.61\pm0.39$, consistent with the mass-concentration relation
found in cosmological simulations.
