Showing up to your hotel after a long flight and having to figure out car rental on the spot is annoying, and your wife's already tired and ready to relax instead of dealing with paperwork. Getting everything sorted before you leave home means one less thing to deal with when you land. You should look at rental cars in Milan here
https://getrentacar.com/en-US/italy/milan . The whole process is way smoother when you deal with local owners in Italy instead of some big rental chain, they're actually flexible about pickup times and can adjust things if your flight gets delayed. You'll have a real person to contact instead of calling some customer service line.