  We study galactic enrichment with rapid neutron capture (r-process) elements
in cosmological, magnetohydrodynamical simulations of a Milky Way-mass galaxy.
We include a variety of enrichment models, based on either neutron star mergers
or a rare class of core-collapse supernova as sole r-process sources. For the
first time in cosmological simulations, we implement neutron star natal kicks
on-the-fly to study their impact. With kicks, neutron star mergers are more
likely to occur outside the galaxy disc, but how far the binaries travel before
merging also depends on the kick velocity distribution and shape of the delay
time distribution for neutron star mergers. In our fiducial model, the median
r-process abundance ratio is somewhat lower and the trend with metallicity is
slightly steeper when kicks are included. In a model 'optimized' to better
match observations, with a higher rate of early neutron star mergers, the
median r-process abundances are fairly unaffected by kicks. In both models, the
scatter in r-process abundances is much larger with natal kicks, especially at
low metallicity, giving rise to more r-process enhanced stars. We experimented
with a range of kick velocities and find that with lower velocities, the
scatter is reduced, but still larger than without natal kicks. We discuss the
possibility that the observed scatter in r-process abundances is predominantly
caused by natal kicks removing the r-process sources far from their birth
sites, making enrichment more inhomogeneous, rather than the usual
interpretation that the scatter is set by the rarity of its production source.
