We study the interplay between long-range electron-phonon and electron-electron interactions in electrostatically doped two-dimensional semiconductors, including interlayer couplings in van der Waals heterostructures. We evaluate the effects of those interactions on transport properties by writing dynamically coupled Boltzmann equations for the electrons and for the electrodynamically active excitations. We develop a theory with a general validity, and apply it both to simplified parabolic models, and to the realistic BN-encapsulated graphene system which we present in an accompanying paper [Dinar et al. ArXiv:2604.00678 (2026)]. We show that dynamical screening effects are of fundamental importance in order to correctly describe the electronic transport properties of two-dimensional materials, and in particular the scattering from polar phonons, whether those come from the semiconductor itself or the surrounding layers.