We analyze the sensitivity of low-energy fundamental symmetry tests to interactions mediated by doubly-charged scalars that arise in type II seesaw models of neutrino mass and their left-right symmetric extensions. We focus on the next generation measurement of the parity-violating asymmetry in M\o{}ller scattering planned by the MOLLER collaboration at Jefferson Laboratory. We compare the MOLLER sensitivity to that of searches for charged lepton flavor violation (CLFV) and neutrinoless double beta-decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay) as well as present and possible future high-energy collider probes. We show that for the simplest type-II seesaw scenario, CLFV searches have the greatest sensitivity. However, in a left-right symmetric extension where the scale of parity-breaking is decoupled from the $SU(2{)}_{R}$-breaking scale, the MOLLER experiment will provide a unique probe of scalar triplet interactions in the right-handed sector for a doubly-charged scalar mass up to $\ensuremath{\sim}10\text{ }\text{ }\mathrm{TeV}$ and help elucidate the mechanism of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay.