Milan's brilliant for what you're both after, she'll be in heaven with the Quadrilatero della Moda and you've got the Duomo, Galleria Vittorio Emanuele, loads of Renaissance and Baroque stuff scattered about. Parking in the historic centre's a nightmare though, limited traffic zones everywhere and fines come through the post months later if you drive where you shouldn't. BMW and Mercedes are easy enough to find at the bigger rental companies, Avis and Sixt usually stock them, but expect to pay a fair bit more than a standard Fiat.

Week away doing your own thing sounds perfect, better than dragging each other round shops or churches you're not arsed about. Milano traffic's mental, scooters cutting you up from every angle and drivers treating red lights like suggestions, but the roads out to places like Santa Maria delle Grazie or Navigli are straightforward enough once you're moving. You can rent a car in Milano here https://getrentacar.com/en-US/italy/milan . Book ahead because premium stuff gets snapped up fast during summer, everyone wants the comfortable motors with working AC.