An exactly solvable sp(4) algebraic approach extends beyond the traditional isospin conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that includes proton-neutron (pn) and like-particle isovector pairing correlations plus significant isoscalar pn interactions. The model yields an estimate for the extent to which isobaric analog 0+ states in light and medium mass nuclei may mix with one another and reveals possible, but still extremely weak, non-analog beta-decay transitions.