We perform neutron diffraction and quasi-elastic neutron scattering (QENS) to probe hydration water structure, and dynamics down to supercooled temperatures, of a concentrated amphiphilic peptide system with the co-solvents glycerol and dimethyl sulfoxide. We find that the kosmotropic co-solvent glycerol preserves the hydration structure near the peptide that is observed in the water solvent alone, that in turn preserves the dynamical temperature trends of two water relaxation processes--one corresponding to a localized relaxation process of the peptide bound surface water and a second relaxation process of the outer hydration layers. By contrast the chaotropic co-solvent, by disrupting the hydration layer near the peptide surface, eliminates the inner hydration layer relaxation process induced by the peptide, to show a single time scale for translational water dynamics.