Hello, I’ve lived in both with young kids.
Why don’t you put them in Italian preschool? They’re young enough to pick up the language with no effort, and that’s good for their development even if you don’t plan on staying long term. In Monza all private preschools are Catholic, however, in Milan there’s a lot more choice. For the public schools you will need to register and select your choice of school the year before they start. Most people go to the school nearest their home, you can apply outside your district but you won’t be a priority for a place.
The International School in Monza doesn’t have a great reputation, they prioritise money over quality of education, but it’s probably more of a problem for later years. I don’t think there are any bilingual schools left in Monza, maybe a couple of nurseries but the quality is hit and miss.
In Milan there is English only preschool at the BSM (pricey), St Louis, the ISM (both just as pricey) and there is bilingual at the Andersen school (less expensive). In Milan too a lot of bilingual nurseries have sprung up but again, the quality varies a lot.
If you’re thinking of having your baby here, the antenatal care is more thorough than the U.K. although the birth is more medicalised. Healthcare is good on the whole, plus many Italian contracts have private healthcare schemes included. Will you be on a local contract? If not you’ll need to pay for healthcare separately, I seem to remember my self-employed friend had to pay something like €750 a year for her health card and thus access to public healthcare services. Mind you that was many years ago so who knows what it is now.
If you live in Milan you won’t need a car, especially in the centre it’s a pain because of the congestion charge. There are a lot of car sharing schemes which are reasonable. Alas this hasn’t reached Monza, which despite being only 15km from Milan in many ways is light years behind.
Friends-if you have small children you will make friends. Do you speak Italian? Most Milanese speak some English, at times very well, but Italian will help a lot. There are expat groups but they do tend to be full of trailing spouses who don’t work and organise coffee mornings at 10am when most of us with a job are at work. This is very true for Monza, a bit less so for Milan. I’m no great expert, I tend to shy away from these groups, my experience was from being invited along to coffee mornings and the like when people heard me speaking English to DD. When I was young, free and single I used to go out for after work aperitivi with friends and neighbours and met loads of people that way too. Italians are happy to chat, or at least that’s been my experience (still is).
Sorry for the huge ramble, if you need to know anything specific then maybe PM me.
Milan is a great city, there is loads to do and it’s got even more cosmopolitan in the last few years (before lockdown anyway). Monza is pretty and has a lovely park and the royal palace, but compared to Milan it is quite provincial. Plus of course you’re only a short drive from the lakes and mountains for hiking and skiing.