We study the effective interaction between impurities which can tunnel separately between two or more wells and which couple via Coulomb interaction to the conduction electrons of the host metal. The effect of the electronic environment on the impurity dynamics is analyzed by means of a renormalization-group method based on a path-integral formulation of the problem. In the tight-binding limit, the most important paths are those where the system stays most of the time in a given configuration with occasional tunneling processes. The intrinsic asymmetry between configurations arising from the long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) --type interactions and the nonquadratic spatial dependence of the long-time retarded coupling creates the need for a generalized scaling scheme which, when applied to the formally similar problem of a spin chain with long-range 1/${r}^{2}$ interactions of arbitrary spin dependence, can account for the presence of symmetry-breaking terms. To understand the interplay between energy bias and hopping energy, an analysis is provided of the time scales for a particle in an asymmetric double well. For the double-impurity case, a crossover is found between a high-temperature or large-separation regime, where impurities behave as independent, and a low-temperature and short-distance regime, where correlated tunneling is established between the most favorable configurations. In this regime the dynamics becomes very sensitive to the geometry and localization effects tend to be enhanced. For many-impurity systems, it is proposed that, at low temperatures and high concentrations, oscillatory long-range interactions and renormalization by low-energy electronic excitations conspire to reduce or even totally suppress the tunneling activity.