We prove convergence, with estimates of the rate of convergence, of iterative schemes for discretized versions of systems of parabolic quasi-variational inequalities (QVI). These parabolic QVI arise in problems of stochastic optimal control with discrete control actions (switchings) where the cost functional involves discrete switching costs in addition to continuous rates of cost. We consider two kinds of discretization: discretization with respect to the space variables, and discretization in both time and space.