Onward from Milan?

From Milan’s Malpensa (MXP) airport, hop on the train to Milano Centrale and transfer there to Varenna-Esino (2h 15m) on Lake Como. You can walk around the town and then hop on a ferry to Bellagio (15-minutes) for the day. The next day take a train to Florence, but you’ll have to connect again in the Milano Centrale station (3h 30m). Unfortunately, hotels will be expensive but it’s worth one day and night.
Another idea is to take a train from the airport in Milan to Verona Porta Nuova station (2h 45m). You’ll still need to transfer at the Milano Centrale station but you can take a direct train from Verona to Florence (1h 45m) departing at 8:52a.

The trip from Milan to Florence is very rapid on one of the Freccia trains--just under 2 hours for a distance of over 200 miles. That is accomplished by making very few stops. If you opt to spend the night in a town between Milan and Florence that's not on the Freccia line, you will add very significantly to the total time you spend moving from Milan to Florence. I imagine you don't want to do that. At a quick glance it appears that all the Milan-Florence trains stop in Bologna, which has a huge historic district, unfortunately about a 20-minute walk from the trains station. Some also stop at the smaller city of Reggio d'Emilia--where I've never been, but Google Maps indicates the Reggio d'Emilia AV station is about 2 miles from the historic center. Both locations are disappointing from the standpoint of getting to your hotel quickly and then being able to walk around a bit in an interesting area.

If you're just looking for an inexpensive place to crash, Reggio d'Emilia may be best unless you'll be making this stop on a weekend. I've found weeknight hotel rates in Bologna not to be inexpensive. I do like the city very much, however.

The thing is, Reggio d'Emilia is a 44 minutes beyond Milan and just barely over an hour short of Florence. Is it really worth the hassle of stopping your journey such a short distance from where you want to be? You'll already be about 2/3 of the way to Florence (in terms of travel time).

Another possibility would be to look for a hotel in one of the smaller towns you'll be passing through on the regional train between the airport and Milano Centrale. That's almost a 1-hour ride in itself. I am totally unfamiliar with those towns. Hotels, if available, might be cheaper. Doing that would mean you'd have to start Day 2 with a more-than-2-hour ride to Florence. On the other hand, with an overnight stay north of Milan on your arrival day, you'd be pretty safe in buying the Milan-Florence ticket for Day 2 ahead of time, which would save a lot of money if you made that purchase when the Freccia tickets for your travel date initially went on sale.

The train ride between Milan and Florence is short, I would try to press on... Especially since you'll probably arrive in the morning if you come from America.
If you really don't want to, then perhaps look at hotels in Saronno? It's a town with a stop on the Malpensa Express. Boring in itself, but if you have the energy you could spend the afternoon / evening in Como town, a short train ride away.

Why wouldn’t you spend at least a night in Milan?

A few years ago we did the trip US to Milan to Florence in one day. It was not a problem. Just be sure you make train reservations allowing for any flight delays. We took an afternoon train which gave us time to have lunch and explore the cathedral in Milan. The next day we had a full day in Florence instead of just a half day.

Thank you for the replies, everyone. Sounds like we may be able to push on from Milan on arrival day after all without much of a headache.

As to why not spend at least a night in Milan—the point of the post is that the hotels in Milan are significantly more expensive than in the other places we want to visit, and Milan is not of particular interest to us.

Milan is great for a night! Head down to the Piazza del Duomo and start wandering around from there - you'll be pleasantly surprised at what you'll find. You should definitely try to get a ticket to see The Last Supper. We've done two 1 nighters in Milan due to travel logistics and look forward to returning.

I suspect that hotel prices in Milan are so expensive is that there is some kind of trade show or convention going on when you arrive. Also, arriving in the morning, you won't be able to get into a room until later in the day. Since your kids will be paying half price on a fast train to Florence, you might consider going business class for more room on the train, currently 154 EUR Base fare for 1 adult and 2 kids under 15. Considering that the train from Malpensa to Milano Centrale is 50 minutes, 1 hour and 55 minutes more to get to Florence is not bad.