Analysis of interaction forces when probing a silica core-polyelectrolyte brush shell nanoparticle, adsorbed on a silica substrate and bathed by aqueous electrolyte solution, with an ultrasharp atomic force microscopy (AFM) tip provides a spatially resolved map of heterogeneous mechanical properties across the nanoparticle. The deformation of the brush is mainly compressive when probed directly above the nanoparticle centre and mainly deflective when probed at a finite horizontal distance away from the centre. The brush is significantly stiffer against compression than against deflection, and ionization of the brush has a greater stiffening effect against compression than deflection. Whereas a height image of the core-shell nanoparticle was unremarkable, showing a monotonic decrease in height with increasing horizontal distance from the centre, brush deformation, energy dissipation and adhesion displayed local minima over the centre and maxima at a finite horizontal distance away from the centre, corresponding to a position near the rigid core nanoparticle edge. The different response to brush deformation depending on the angle of probing is relevant to the interactions of brush-decorated macroscopic surfaces with submicrometer roughness and to the interactions of brush-decorated nanoparticles with ultrafine structures in their environments.