We investigate the stellar and dynamical mass profiles in the centres of 25 brightest cluster galaxies (BCGs) at redshifts of 0.05 $leq z leq$ 0.30. Our spectroscopy enables us to robustly measure the Gauss-Hermite higher order velocity moments $h_{3}$ and $h_{4}$, which we compare to measurements for massive early-type galaxies, and central group galaxies. We measure positive central values for $h_{4}$ for all the BCGs. We derive the stellar mass-to-light ratio ($Upsilon_{star rm DYN}$), and velocity anisotropy ($beta$) based on a Multi-Gaussian Expansion (MGE) and axisymmetric Jeans Anisotropic Methods (JAM, cylindrically- and spherically-aligned). We explicitly include a dark matter halo mass component, which is constrained by weak gravitational lensing measurements for these clusters. We find a strong correlation between anisotropy and velocity dispersion profile slope, with rising velocity dispersion profiles corresponding to tangential anisotropy and decreasing velocity dispersion profiles corresponding to radial anisotropy. The rising velocity dispersion profiles can also indicate a significant contribution from the intracluster light (ICL) to the total light (in projection) in the centre of the galaxy. For a small number of BCGs with rising velocity dispersion profiles, a variable stellar mass-to-light ratio can also account for the profile shape, instead of tangential anisotropy or a significant ICL contribution. We note that, for some BCGs, a variable $beta_{z}(r)$ (from radial to tangential anisotropy) can improve the model fit to the observed kinematic profiles. The observed diversity in these properties illustrates that BCGs are not the homogeneous class of objects they are often assumed to be.
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