Curious from where are you flying into Milan? I'm in Chicago and there is only 1 direct flight, at 10:30pm.
In Milan you have a good itinerary. I'd suggest the hop on/off bus to get a lay of the land. Staying near the train station is convenient. The food is good most places.
I don't know the lake region, but those who do rave about Bellagio.
Venice needs no explanation: just walk and observe.
7 days in Florence is lovely, and you could spend them all in the city. If you and family are renaissance art aficionados. One overlooked museum is the Bargello, mostly sculpture, Donatello, Cellini, ecc
If you appreciate architecture, the Laurentian library (Michaelangelo) is elegant, next to San Lorenzo Church. It isn't always open, you must research. Cappella Medici more ostentatious, but beautiful. Churches overlooked: Santo Spirito (Brunelleschi. In the Oltrarno area across the bridges),
The rest (Uffizi, Accademia, Santa Maria Novella, Santa Croce...) are obvious visits.
You may want to book a tour of Tuscany,. I believe buses can be had to: San Gimignano, Volterra, Chianti villages: Greve, Pantano, Castellina. My favorite area is further south: Siena, Montepulciano, Pienza, San Quirico, Montalcino. The Val D'Orcia Is spectacular! Further south still, but will be out of your way, maybe next time when you include Rome, are Orvieto and Assisi. You could perhaps book tours from Florence? Just suggestions. Buon viaggio