We present a study of the lateral transport of a two-dimensional electron gas (2DEG) in a modulation-doped polar heterojunction (HJ). In contrast to previous studies, we assume that the Coulomb correlation among ionized impurities and among charged dislocations in the HJ is so strong that the 2DEG low-temperature mobility is not limited by impurity and dislocation scattering. The mobility, however, is specified by alloy disorder scattering and combined roughness scattering, which is the total effect induced by both the potential barrier and polarization roughness. The obtained results show that the alloy disorder and combined roughness scattering strongly depend on the alloy content and on the near-interface electron distribution. Our theory is capable of explaining the bell-shaped dependence of the lateral mobility on alloy content observed in AlGaN/GaN and on 2DEG density observed in AlN/GaN, which have not previously been explained.