Aside from the tax aspect, living in Italy with a family is pretty miserable. I lived there, and experienced it. Other friends have done it as well and told me the same thing.
Aside from the lack of childcare, there is no child infrastructure (no children park where they can get some fresh air and exercise for instance), society is old, ageing, municipalities are governed by insufferable boomers that absolutely hate children. Every town is car-centric, even the old ones clearly not designed for this. There is no public transportation. Walking in most of the towns is a struggle in itself, due to the insane︀ parking everywhere.
You'll have to get angry daily about the wankers and the silly geese︁ with Vuitton bags that park their Fiat 500 on the side walk and prevent you︂ from walking freely with your pram. The Italian health system is overloaded with old people︃ coming to the hospital for any reason, and they always have the priority over the︄ young, the pregnant women, and the children. Private health services are expensive and doctors are︅ so-so.
People will look down on you because you have more than two children, send︆ you mail because you make noise during the day. You'll be kicked out of restaurants︇ more or less politely because the local boomers don't want to deal with the potential︈ annoyance. Yeah, you'll see people saying nice things on some occasions, however the crude reality︉ is that society has given up with the idea of having children, and you'll feel︊ it very well every day. The amount of old people with no grandchildren is heart-crushing,︋ and I witnessed a few times old ladies almost breaking up in tears when they︌ could hold my son's hand.
Add the African immigration that flocks in, and really, you︍ don't want to live in Italy with your family. Just go there on holidays.