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Metal-poor stars in the Milky Way (MW) halo display large star-to-star dispersion in their r -process abundance relative to lighter elements. This suggests a chemically diverse and unmixed interstellar medium (ISM) in the early universe. This study aims to help shed light on the impact of turbulent mixing, driven by core-collapse supernovae (cc-SNe), on the r -process abundance dispersal in galactic disks. To this end, we conduct a series of simulations of small-scale galaxy patches which resolve metal-mixing mechanisms at parsec scales. Our setup includes cc-SNe feedback and enrichment from r -process sources. We find that the relative rate of the r -process events to cc-SNe is directly imprinted on the shape of the r -process distribution in the ISM with more frequent events causing more centrally peaked distributions. We consider also the fraction of metals that is lost on galactic winds and find that cc-SNe are able to efficiently launch highly enriched winds, especially in smaller galaxy models. This result suggests that smaller systems, e.g., dwarf galaxies, may require higher levels of enrichment in order to achieve similar mean r -process abundances as MW-like progenitors systems. Finally, we are able to place novel constraints on the production rate of r -process elements in the MW, $6\times {10}^{-7}{M}_{\odot }\,{\mathrm{yr}}^{-1}\lesssim {\dot{m}}_{\mathrm{rp}}\ll 4.7\times {10}^{-4}{M}_{\odot }\,{\mathrm{yr}}^{-1}$ , imposed by accurately reproducing the mean and dispersion of [Eu/Fe] in metal-poor stars. Our results are consistent with independent estimates from alternate methods and constitute a significant reduction in the permitted parameter space.