We present WFPC2 F450W, F555W, and F814W photometry for three early-type galaxies with kinematically distinct cores (KDCs), namely NGC 2434, NGC 7192, and IC 4889. For these three objects we present the B, V, and I nuclear surface brightness, isophotal, B-V and V-I profiles and derive the deprojected luminosity densities. The three KDCs have nuclear cusp slopes [gamma(v)] in agreement with the [gamma(v)] versus absolute magnitude (M-v) relation defined by kinematically normal galaxies and by other KDCs. NGC 7192 contains an unresolved blue nuclear spike of V similar or equal to 22.2, B-V similar or equal to 0, and V-I similar or equal to 0.7. We use these new data, and the WFPC2 photometry for 15 KDCs presented in Carollo et al., to investigate several open questions related to the nuclear properties of this class of galaxies, We find the following : 1. If there is a direct effect of environment on the nuclear properties of KDCs, this is similar to that acting on kinematically normal galaxies. Dynamically hot systems preferentially have low nuclear densities and shallow cusps when in clusters and high nuclear densities and steep cusps when in the field. The highest nuclear densities are reached in the field. 2. Within the limits imposed by the angular resolution of WFPC2 data and by the presence of nuclear dust, KDCs have symmetric nuclei. This result is independent of environment, form of the nuclear light profiles, nuclear morphology, and presence of an unresolved, likely nonthermal, central source. 3. The known Mg-2 index-enhanced KDCs might not be all nuclear disks embedded in anisotropic stellar bodies. Three galaxies, namely NGC 2434, NGC 7192, and NGC 7626, do not show any photometric signature for a nuclear disk associated with their Mg-2-rich KDCs. The Mg-2-rich KDCs may arise from a large variety of morphological (and dynamical) structures, possibly indicating a variety of star formation and dynamical histories. 4. The "delta-delta" correlation between the residuals of the [gamma(v)] versus M-v relation, and Mg-2 versus M-v relation, is approximately at the 3 sigma level, which implies a residual dependence of the cusp slope [gamma(v)] on the Mg-2 line strength: the higher the Mg enrichment, the shallower the nuclear cusp slope. 5. The Mg-2-enhanced KDCs do not occupy any special location in the correlation between [gamma(v)] and Mg-2 (correlation that worsens significantly if for these KDCs one considers the Mg-2 value extrapolated from the outer galactic regions). They also do not occupy any special location in the "delta-delta" correlation above. Therefore, our data suggest that the processes that made the KDCs in the host galaxies (on scales of approximate to 1 kpc) also rebuilt their central structures (i.e., the nuclear cusps on scales less than or similar to 100 pc). Finally, our work adds further support to the previous findings (Forbes et al.; Carollo et al.) that KDCs show little or no evidence for any photometric difference compared to other early-type systems of similar luminosity.
