<p>We investigate the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. We derive robust integral form and pointwise second-order necessary optimality conditions involving integrals with respect to certain reference probabilities, under specific compactness and monotonicity. Both the drift and diffusion terms depend on the control, and the control regions are assumed to be convex because saddle point analyses are crucial for deriving the variational inequality with a common reference probability for any admissible control. Other main technical components for the integral type conditions include weak convergence arguments and the minimax theorem, while the pointwise conditions involve the Clark-Ocone formula and Lebesgue differentiation type theorem. Additionally, an example is provided to demonstrate the motivation and effectiveness of the results.</p>