I am glad you came to tripadvisor for some info. I would hate to see your family come to Italy and spend a lot of time packing and unpacking every few days. You can still see a lot by choosing 3 places to base yourself. If you stay in Venice you can do a day trip to Verona, for example. In the Lakes area you can take a boat to see other towns.
I would try to mix it up a little - not just big cities. Mountains, lakes or countryside with one or two big cities. No one can see all of Italy's beauty, history, major sites in one visit. You will have to prioritize and decide what you and your family will most enjoy given it will be hot and crowded at many of these places.
If you are flying in to Milan it makes sense to spend one night there.
I hope we hear from you again. Let us know how your plans are coming and maybe we can give you some help.
I really like Rick Steve's for travel info.. He does tours and writes travel guides. Here is a really good video he did on Italy and what there is to see.
Also, are you and your family traveling on your own or with a tour group?
Anyway, don't be put off by replies that seem unfriendly or condescending. That unfortunately is fairly common. Good luck and I wish you a wonderful trip!