Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting appropriate functions of the general variable separation solution.