Park & Ride into Milan?

just a thought, but have you considered catching the airport train into milan, look around,( leave you luggage at centrale?? not sure) then pick up your rental car from the linate airport that is about 8kms ( short taxi ride) from milan centrale its also on the 'right' side of milan t o continue your journey.

may be an option???

You could spend the night in Milano and have a fresh start the next morning.

There are large parking silos linked to metro lines at Lampugnano, Famagosta, Cascina Gobba to name just the few coming to my mind. The one at Famagosta looks to be the easier as there is an highway exit directly entering the parking. But in my opinion spending the night on an airplane over a few time zones, then spending the day touring, then driving several hours looks to me very tiring.

In all my trips to Europe (about 12, I think), I have never been in condition to start a 3-hour drive at any time on my arrival day, much less in the mid- to late afternoon. I can't imagine being comfortable doing that, because I seldom sleep much on the plane. I'd even have trouble taking in the rental agent's instructions on how to find a convenient park-and-ride lot.

It's winter and the A1 freeway in Po Valley between Milan and Bologna will likely have heavy fog conditions, especially after dark.
The A1 freeway between Bologna and Florence goes through the Apennines mountain range and could have icy conditions.
You will be experiencing all of that while jet lagged.
My suggestion would be to stay in Milan the first night, rent the car the next morning in the city, and make it to Montecatini the next day. I would even suggest to travel by train to Florence and rent a car in Florence.

Wow, thank you all for your very good suggestions! I see now that it would be not a great idea to make the drive so we'll plan to stay in Milan the first night. We need to pick up our rental car at the airport, so maybe a hotel just outside Milan, take the Metro in, then leave the next morning for Montecatini Terme. It will be our only opportunity to fully experience Milan because our return is on a Monday -- and I also already have purchased tickets for The Last Supper for Wednesday.

Many thanks to you all - Linda

As I've just read on tripadvisor: I'm still wondering why would anyone drive through the mountains at 100 kms/h during the winter, when there is a train that runs under them at 250.

But of course it's your choice: note that the new mountain section of the A1 motorway after Bologna is listed as "Direttissima" on signs, while the old route is the "Panoramica". The Direttissima runs mostly in new tunnels. I think that the only reason to take the old Panoramica is that it's "trucks free" these days.
On both there are many speed traps.

Do not leave anything in the trunk anywhere in Italy, it doesn't matter if it can be seen or not from the outside.

What day are you arriving in Milan? You have a reservation for the Last Supper on Wednesday, morning or afternoon?
Might suggest taking the train to Milano Centrale from Malpensa. There are many good hotels near the station. Check in and relax, tour Milan, see the Last Supper if an afternoon appointment. Next day, take a train to Montecatini Terme. There are Europecar and Sixt rental locations near the train station. Mid-afternoon train costs about 40 EUR per person. and it will take 2 hours and 36 minutes with a train change in Florence.
The train cost is the price now, bought on-line, nonrefundable, not changeable.

Via Michelin estimates that it is 3 hours and 30 minutes driving and will cost about 60 EUR, 30 for gas and 30 for tolls. Plus you have the time to back-track to Malpensa to rent the car. And as was pointed out, lots of robo-speed traps to send love letters to speeders on their return home. Plus the service fees that the rental companies put on the credit card you used to rent the car for telling the police who rented the car, one fee for each ticket.

As mentioned above, the best option would actually be to go to Montecatini by train (same day or next day, is up to you), and rent a car there.

It makes no sense to go back to Malpensa (very far from Milan city center) to pick up the car. In the time it takes you to go back to Malpensa and have a car in your hands, the train will get you almost in Florence.

There are rental offices in Florence and Montecatini (Europcar is for sure present next to the station in Montecatini).