Florence - 1 day with kids

Visiting both the Academy and the Uffizi on the same day is easy. Be sure to get appointments or advance tickets so you don't waste time standing in lines.

You might want to consider going to the Bargello. Not only are there some major artworks (Donatello's David for example) but it also usually far less crowded. The collection covers sculpture, ceramics, Islamic art, armor and period weapons. The building is a fortress and served as the model for the later Palazzo della Signoria. It's the kind of place that might appeal to a wider range of kids than one of the more famous museums plus it's not huge so a thorough walk through won't take all day.

Regarding the duomo? Personally, I think the exterior is much, much more impressive than the interior. With such a short time to see the city, I wouldn't stand in a long, hot line with 3 kids to do that one. The baptistry is a different story: the interior is by far the star of that show.

The choice between Uffizi and Accademia is a tough one. The collection at the Uffizi is much larger and takes more time to see - plus offers some impressive views from various spots - whereas the the Accademia has that big, naked guy that's high on darn near ever tourist's list. Your 8-year old, being short, might struggle with seeing over/around the summer crowds so maybe choose the smaller of the two.

Then again, there are alternatives to BOTH for art lovers on tight timelines. The Bargello and San Marco, for instance, are wonderful and will not be as overrun so you might take a look at those? We enjoyed both for their collections and for having fewer bodies to contend with. There's plenty there to engage your teenager without exhausting/frustrating the younger two.

The Duomo Museum would be another option. It is included in your Duomo/Baptistry ticket. There you can see an amazing rebuild of the Duomo facade where the statues - the originals - are closer and easier to see. This is where you will see most of the art that was in the Duomo. There are excellent displays and video that tells the story of the building of the Dumo - specifically Brunellesci's dome. The great choirs(balconies) are also there. On the top floor you can walk outside and view the dome up close. The whole museum can be done in about 1.5 hours.

Get advanced purchase tickets for the Academia (it says how to do that in Rick's book). get an early morning time so crowds will be minimal. Don't go to Florence and not see the real statue of David.
Any 12 and 8 year old worth his/salt should know how to say excuse me and worm their way to the front!!
The Bargello is also a good option

Your 8-year old, being short, might struggle with seeing over/around
the summer crowds

To clarify, I meant around the adults crowding in front of other works, particularly at the Uffizi. "David" is high on a pedestal so is not difficult for short folks to see. LOL, my favorite "David" is at the Borghese in Rome: if you're doing the Eternal City on this trip, THAT museum is a must for art lovers, and it has excellent crowd control. It's also easily done in the 2-hour time slots you're allowed, and the building itself is fascinating.