Pisa and Leaning Tower easy day rip from Florence as is Lucca - wonderful ancient walled town - could easily do both in one day.

Not dealing with jet lag is a big factor. If you decide you really want a taste of both cities, Susan P's idea is a good one.

Or stay in Rome and day trip by train to Florence for a day - trains take little more than an hour. Can see most of major things.

Both the Uffizi and the Accademia in Florence sell timed entry tickets. In late May these were sold out several days in advance. It may be possible to wait in line to get in (I don't know), but that's not a good use of your limited time. It may get worse over the summer if that's when you're going, so plan ahead. I don't know the official website but it's easily found online. This is likely the situation with many other places you may want to visit in Rome as well, including museums, ancient sites (Colosseum, Forum). The exception being churches in Rome or the Vatican which you can enter without a ticket. There is a security screening to pass through to get into St. Peter's Basilica, and the line can be long, but it generally moves pretty quickly. Visiting these popular places early in the day before busloads of tourists descend en-masse will help you avoid getting mobbed.

The Uffizi is a huge museum, focused on Italian Renaissance painting, mostly of religious subjects. It's also very crowded, even though they limit entries. It's not easy to do a quick visit. Unless your daughter is passionale about that sort of art, I would give priority to other museums.

The Accademia is much more manageable, although apart from Michelangelo's David, there's not a whole lot else to see there.

The Bargello is a sister museum of the Uffizi, focussed on sculture. It's never crowded, and doesn't need reservations.

The Museum of San Marco, in a former convent, has the monks' cella decorated by marvelous frescoes by the the great artist, known in Italian as the Beato Angelico; in English he's more known as Fra Angelico. This is another crowd-free museum.

The Museum of the Duomo has a great collection of art that was once in the Duomo, and a lot of interesting displays of the history of the building, and the construction of its great dome.

tamaraten - If i were a travel agent who wanted your repeat business I'd not sell you that itinerary. I'd advise you to leave Florence for the future or be satisfied to get just a taste on a day trip. It's not really "grueling" unless you try to cram in too much.