Aims. Interacting galaxies show unique irregularities in their kinematic structures. By investigating the spatially resolved kinematics and stellar population properties of galaxies that demonstrate irregularities, we can paint a detailed picture of the formation and evolutionary processes that took place during their lifetimes. Methods. In this work, we focused on galaxies with a specific kinematic irregularity: a kinematically distinct stellar core (KDC). In particular, we considered counter-rotating galaxies in which the core and main body of are rotating in opposite directions. We visually identified 11 MaNGA galaxies with a KDC from their stellar kinematics, and we investigated their spatially resolved stellar and gaseous kinematic properties, namely the two-dimensional stellar and gaseous velocity and velocity-dispersion (σ) maps. Additionally, we examined the stellar population properties, as well as spatially resolved recent star formation histories, using the Dn4000 and Hδ gradients. Results. The galaxies display multiple off-centred symmetrical peaks in the stellar σ maps. The gaseous velocity and σ maps display regular properties. The stellar population properties and their respective gradients show differing properties depending on the results of the spatially resolved emission line diagnostics of the galaxies, with some but not all galaxies showing inside-out quenching. The star formation histories also largely differ based on the spatially resolved emission line diagnostics, but most galaxies show indications of recent star formation either in their outskirts or core. Conclusions. We find a distinct difference in kinematic and stellar population properties in galaxies with a counter-rotating stellar core, which depends on its classification using spatially resolved emission line diagnostics.