First time to Italy

Hi everyone, we are planning a trip to italy with 2 kids who will be 3years and 15 months when we visit at end of August.
me and my husband want to visit Florence, Pisa and Venice. But we want to keep our trip centric around kids so they get to enjoy and visit some parks in between.
we recently took them to Portugal and Porto was amazing but we found Lisbon too touristy with kids.
can you please suggest 2 base cities to enjoy Florence and Venice, we will be flying from USA.
gondola ride is a definite to do on my list.
our trip will span over 9-10 nights.
how much time should we devote to each place so we enjoy the city and also feel relaxed. we like to do half day sightseeing, then give kids a break before doing another 2-3 hours of outdoors.
Thanks.
 
After reading many other forums, it seems we should not visit Venice with such small kids.

Now we are considering flying into Rome, how do we get to Florence from Rome? Train?
And how to reach the train station in rome from airport?

Any tips on which city to use as a base would be highly appreciated. Since we will fly back from Rome, we might spend 1-2 nights in Rome but for remainder of the trip we would prefer to keep one base city and explore as much Tuscany as possible.
 
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