Two-fluid nonlinear MHD simulations using the TM1 code demonstrate that the formation of magnetic islands at the top and bottom of the H-mode pedestal, together with the strong screening of resonant fields in the gradient region of the pedestal, can account for ELM suppression and density pump-out by n = 2 Resonant Magnetic Perturbations (RMPs) in lowcollisionality DIII-D ITER Similar Shape (ISS) plasmas. Using experimentally relevant transport coefficients, neoclassical resistivity, electron collisionality, and RMP amplitudes, nonlinear MHD simulations reproduce the observed level of density reduction (density pumpout) in DIII-D due the formation of narrow magnetic islands and resulting enhanced collisional transport in the resistive foot of pedestal. For large amplitude RMPs (Br/Bt>1´10 -4 ) simulations predict field penetration and pressure reduction at the top of the pedestal consistent with experimental observations at the onset of ELM suppression. The predicted reduction in the height and width of the pedestal by magnetic island enhanced transport provides a quantitative mechanism for the stabilization of the Peeling-Ballooning Mode (PBM). Importantly, these simulations predict strong screening of resonant fields in the steep gradient region of the pedestal due to strong E´B and diamagnetic flows. However, if the plasma resistivity is made artificially larger (~10X) than neoclassical, the simulations predict magnetic stochasticity throughout the plasma edge and the collapse of the pedestal due to the reduction in the penetration threshold with increasing resistivity. A scaling relation for resonant field penetration at the pedestal top, using several hundred nonlinear simulations, reproduces the density and E´B dependence of the ELM suppression threshold observed in DIII-D. Simulations using ITER model equilibria suggest that the penetration threshold at the top of the ITER pedestal will be much lower than in DIII-D due to the anticipated lower perpendicular flow velocities in ITER, resulting in the weaker screening of resonant fields.