This paper presents a comprehensive stochastic optimization model that seamlessly integrates aggregate electric vehicle (EV) charging demand response with power grid system operations, leveraging the inherent flexibility of EV charging. Our main novel contribution is tackling the problem of uncertainty in the demand characteristics. In our stochastic model, we capture not only unknown user charging patterns but also the effect of a pseudo-randomized mechanism applied to provide differential privacy (DP) guarantees to users whose charging patterns are not disclosed. From a control perspective, the intrinsic randomness of the users charging needs, compounded with randomness introduced by the DP mechanism can easily result in infeasible solutions. To overcome this challenge, we adopt a robust optimal control strategy that encompasses the intersection of potential sampling scenario-based constraints. In addition, to manage the high-dimension of the control action space, we approximate the intersections of the feasible regions with a reduced set of polyhedron constraints. In conclusion, our case studies based on IEEE standard systems demonstrate that the proposed algorithm effectively addresses robustness, scalability, and differential privacy for EV users by dynamically adapting to control the demand response for renewable energy integration while consistently ensuring the privacy of EV drivers.