For solution mappings of parameterized models (such as optimization problems, variational inequalities, and generalized equations), standard stability inevitably fails as the parameter approaches the boundary of the feasible domain. One remedy is relative stability restricted to a constraint set (e.g., the feasible domain), which is our focus in this paper. We establish generalized differentiation criteria that characterize stability and strong stability of a solution mapping relative to a broad class of nonconvex constraint sets. Beyond this class, we give a counterexample that invalidates all known generalized differentiation criteria. Applied to generalized equations, our results yield characterizations of relative stability and relative strong stability of their solution mappings, which are further explicitly specified for affine variational inequalities. Finally, we prove a global relative stability criterion, which provides a different perspective on stability analysis and also generalizes the mean value theorem to set-valued, non-smooth mappings.