Atomic-level simulations are used to examine the structure, thermodynamics, and dielectric properties of (Ba0.8Ca0.2)TiO3-Bi(Mg0.5Ti0.5)O3 perovskites. These simulations demonstrate that mixing is non-ideal between the end-members, and only specific configurations can form at higher Bi(Mg0.5Ti0.5)O3 content. Significant structural relaxations are identified around the Bi and Mg cations. The effect of these relaxations on polarization is investigated and highlights that they disrupt ferroelectric domains in the material, preventing collective polarization mechanisms that links to the experimentally observed relatively flat permittivity-temperature profiles [1].