Renting cars in Milan?

Will you be returning the car in Italy? International drop charges tend to be excruciatingly high.

Have you rented in Italy and are familiar with the expensive costs if you don't know the rules, or is it just that Milan is new?

Are you familiar with the special costs involved with driving in Switzerland?

Where in Switzerland are you planning to go? The experience of having a car in Switzerland varies between mildly annoying and downright infuriating...

If you are dead set on renting a car, then I can't offer information. However, as a general bit of advice, do look into taking the train. European train service is very good, both of you can enjoy the views, the driver isn't stressed, and you don't have the hassle of renting, insuring, and hoping you are not cited for a traffice violation. Just my two cents worth.

You don't mention where in Switzerland you are going. But in general I agree that if you are in Milan and want to go to Switzerland, the train is the best way to get there.

Your other post mentioned a desire to go skiing. If that is the case, you can probably do that by going to Zermatt where there is year round skiing on the glacier, plus due to it high elevation, may have some other slopes open. It is a 3 1/2 hour train from Milan with a single change in Brig. And a car won't help because Zermatt is car-free and can only be reached by train.
https://www.zermatt.ch/en

As mentioned above you are better off taking a train for most Swiss destinations. If you must absolutely rent a car be aware that you must return it in Italy to avoid huge drop off fees.

Be also aware that carrying chains or snow tires is mandatory practically everywhere in Northern Italy from now until April. So make sure you rent those at the rental agency.