Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electronphonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electronphonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS2 monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.