  (abridged) We utilize existing imaging and spectroscopic data for the galaxy
clusters MS2137-23 and Abell 383 to present improved measures of the
distribution of dark and baryonic material in the clusters' central regions.
Our method, based on the combination of gravitational lensing and dynamical
data, is uniquely capable of separating the distribution of dark and baryonic
components at scales below 100 kpc. We find a variety of strong lensing models
fit the available data, including some with dark matter profiles as steep as
expected from recent simulations. However, when combined with stellar velocity
dispersion data for the brightest member, shallower inner slopes than predicted
by numerical simulations are preferred. For Abell 383, the preferred shallow
inner slopes are statistically a good fit only when the multiple image position
uncertainties associated with our lens model are assumed to be 0\farcs5, to
account for unknown substructure. No statistically satisfactory fit was
obtained matching both the multiple image lensing data and the velocity
dispersion profile of the brightest cluster galaxy in MS2137-23. This suggests
that the mass model we are using, which comprises a pseudo-elliptical
generalized NFW profile and a brightest cluster galaxy component may
inadequately represent the inner cluster regions. This may plausibly arise due
to halo triaxiality or by the gravitational interaction of baryons and dark
matter in cluster cores. However, the progress made via this detailed study
highlights the key role that complementary observations of lensed features and
stellar dynamics offer in understanding the interaction between dark and
baryonic matter on non-linear scales in the central regions of clusters.
