We investigate the nature of the broad-band emission associated with the low-power radio hotspots 3C 105 South and 3C 445 South. Both hotspot regions are resolved in multiple radio/optical components. High-sensitivity radio Very Large Array, near-infrared/optical Very Large Telescope and Hubble Space Telescope (HST) and X-ray Chandra data have been used to construct the multiband spectra of individual hotspot components. The radio-to-optical spectra of both hotspot regions are well fitted by a synchrotron model with steep spectral indices ∼0.8 and break frequencies between 1012 and 1014 Hz. 3C 105 South is resolved in two optical components: a primary one, aligned with the jet direction and possibly marking the first jet impact with the surrounding medium, and a secondary, further out from the jet and extended in a direction perpendicular to it. This secondary region is interpreted as a splatter-spot formed by the deflection of relativistic plasma from the primary hotspot. Radio and optical images of 3C 445 South show a spectacular 10-kpc arc-shape structure characterized by two main components, and perpendicular to the jet direction. HST images in I and B bands further resolve the brightest components into thin elongated features. In both 3C 105 South and 3C 445 South, the main hotspot components are enshrouded by diffuse optical emission on scale of several kpc, indicating that very high energy particles, possibly injected at strong shocks, are continuously re-accelerated in situ by additional acceleration mechanisms. We suggest that stochastic processes, linked to turbulence and instabilities, could provide the required additional re-acceleration.