<p>The aim of this contribution is to look into the convergence of solutions for a sequence of two-phase Stefan problems featuring non-homogeneous Robin-type boundary conditions, a mushy region and stochastic multiplicative noise, towards the solution of a related equation driven by a sharp diffusion operator. More precisely, the main result can be seen as a Trotter type result which proves the convergences of the solutions in the natural space where they belong, assuming that we have a graph convergence of the nonlinear operators. The result holds significant potential, particularly giving a framework for problems related to homogenization or to the study of similar equations in critical cases, with sharp non-linearity. Rigorous error bounds are derived for a class of regularizations of the Stefan problem. The theoretical analysis is supplemented with illustrative examples of regularization methods and accompanying numerical experiments.</p>