Abstract The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges–Rovnyak spaces where the defining function is a general non‐extreme rational function. Our results carry over to recently introduced higher order local Dirichlet spaces and thus generalize previously known results in classical local Dirichlet spaces. In this setting, we also investigate random interpolating sequences with prescribed radii, providing a 0‐1 law.