Molecular dynamics simulations of a coarse-grained model with soft, nonbonded interactions and implicit solvent are used to study the temperature- and pH sensitive response of mixed brushes composed of poly(N-isopropylacrylamide) [PNIPAm] and poly(acrylic acid) [PAA] polymers. The model is developed in order to address experimentally relevant, large invariant degrees of polymerization, and nonbonded interactions are expressed via a third-order virial expansion of the equation of state. The choice of interaction parameters for PNIPAm mimics the swelling behavior in water as the temperature increases toward the lower critical solution temperature, T-LCST, and the model captures the pH-dependent response of PAA at fixed ionic strength (IS). For this case, the solvent-mediated Flory-Huggins parameter is adapted to reproduce the experimental pH swelling of the homopolymer brush. Mixed brushes incorporating various amounts of PAA are considered, and the effect of mixing polymers on the response of the mixed brushes to both temperature and pH changes is discussed. Additionally, nanoparticles (NPs) that preferably interact with the PAA portion of the polymers are considered. As a function of their radius and the size of the functional NP-attractive groups on PAA chains, the capability to capture NP and allow them to penetrate inside brushes is studied at various temperatures and fixed pH. Moreover, the kinetics of adsorption and release of NPs is investigated.