Light can exert differential forces on left- and right-handed enantiomers, promising an all-optical route towards chiral resolution and controlled assembly of chiral nanostructures. However, enantioselective optical forces on nano-specimens are challenging to both control and quantify, since their magnitudes are predicted to be sub-piconewton-scale with nanometer-scale spatial variation. Here we demonstrate new methods to both strengthen and visualize these forces using achiral nanostructures. First, we show how plasmonic optical tweezers can enable selective optical trapping of enantiomers. Our technique combines plasmonic optical tweezers with a chiral atomic force microscope (AFM) probe. Illumination of the plasmonic tweezers with left- and right- circularly polarized light (CPL) results in distinct forces on the chiral AFM tip: the total optical forces exerted on a left-handed chiral tip are 10 pN stronger when illuminated with left-CPL than with right-CPL. Additionally, the transverse optical forces on this chiral tip are attractive with left-CPL, but repulsive with right-CPL. We use the AFM tip to map such chiral optical forces over the plasmonic tweezers with 2 nm lateral spatial resolution, showing distinct force distributions in all three dimensions for each handedness. Then, we show how high-index dielectric nanostructures and metasurfaces can increase enantiomer separation yields more than 50 times beyond CPL in free space. Mie theory and a local optimization algorithm indicate that magnetic multipolar Mie resonances supported by sub-micron silicon spheres increase both the circular dichroism signal and Kuhn's dissymmetry factor compared to CPL in free space. Importantly, these enhancements maintain the total molecular absorption rate, enabling efficient selective photoexcitation. Combined, our results suggest that achiral photonic nanostructures can significantly enhance chiral light-matter interactions, potentially enabling controlled enantiopure chemical syntheses, single molecule chiral spectroscopy, and dynamic monitoring of structural changes of chiral molecules with sub-nanometer resolution.