The trending integrations of Battery Energy Storage System (BESS, stationary battery) and Electric Vehicles (EV, mobile battery) to distribution grids call for advanced Demand Side Management (DSM) technique that addresses the scalability concerns of the system and stochastic availabilities of EVs. Towards this goal, a stochastic DSM is proposed to capture the uncertainties in EVs. Numerical approximation is then used to make the problem tractable. To accelerate the computational speed, the proposed DSM is tightly relaxed to a convex form using second-order cone programming. Furthermore, in light of the continuous increasing problem size, a distributed method with a guaranteed convergence is applied to shift the centralized computational burden to distributed controllers. To verify the proposed DSM, real-life EV data collected on UCLA campus is used to test the proposed DSM in an IEEE benchmark test system. Numerical results demonstrate the correctness and merits of the proposed approach.