The dynamics of selective ion solvation in water-methanol and water-dimethylsulfoxide (DMSO) systems is investigated using molecular dynamics simulations. The results are compared with earlier work involving simple dipolar models. Solvation response functions, S(t), are used to follow the energetic relaxation, and particle solvation response functions, P(t), introduced in our earlier work, are used to examine the compositional relaxation of the first solvation shell. Despite the presence of hydrogen bonding, the dynamical behavior in water-methanol systems was found to be very similar to that observed for simple Stockmayer solvents. For the water-DMSO mixtures, it was found that the relative sizes and geometries of the solvent species can have a substantial influence on the preferential solvation process. For positively charged solutes in water-DMSO the physical picture does not differ greatly from the water-methanol case. However, for negative solutes the DMSO component shows only a weak response to the charge, and the solvation process consists largely of water molecules moving slowly to the solute through an essentially static DMSO medium. Our results also illustrate that the usual solvation response function, which depends on the total solute-solvent energy, is not a very sensitive probe of selective solvation dynamics. The contribution to the total solute-solvent energy from preferential solvation is very small compared to the contributions from the relatively rapid solvent reorientation and electrostriction processes. The dynamics of selective solvation is evident in species-specific functions but these are not obtained experimentally. The insensitivity of the usual solvation response function has been noticed in recent experimental studies, and an alternative function that appears to be more sensitive to the solvent composition near the solute has been suggested.