15 nights is not really enough to include two areas that take a long time to get to/from. Instead of seeing how much you can fit in, start by looking at each destination and thinking about how much time you want to be there.
Venice - do you want to spend a day going to the islands? Do you want to visit one or more of the grand palaces and art museums? Or do you just want a day to see the highlights and get a taste of the city?
Florence - how much time do you want to spend seeing the great paintings, frescoes, sculptures in the many museums and churches? Do you want to take day trips (Siena, Lucca, wine tour)?
Rome - ditto.
Now, how much time is left over? And what do you really enjoy seeing and doing? Everyone's interests are different. Fortunately Italy has tons to offer for every preference.