difficult to play on the official soccer fields :/
Ciao Katri,
I understand the difficulty in getting two boys to be more interested in museums or history so it might be a bit tough, but there are some attractions you should consider that they might like:
1. Palazzo Vecchio: has itineraries for kids, where the palace is presented by someone dressed up as a historical persona and the kids have activities to do.
2. the Galileo science museum: kids can touch some instruments that show how some things work.
You can see a few more ideas at the end of this article:
http://www.visitflorence.com/itineraries-in-florence/a-weekend-in-florence.html
Also the Strozzi Palace generally offers some interactive, children's activity related to the current exhibit taking place. You can read more here:
http://www.palazzostrozzi.org/Path.jsp?idPath=13
Finally, the book shop at Palazzo Vecchio has a good deal of books for kids that present the city and locations with sticker books, coloring books and more... I think you should get some as soon as you arrive and see if through that they are interested in seeing some of the locations, even if they don't care much about history or art in general, they might have fun trying to spot in real life what they see in the books. I recall seeing one that made going around a treasure hunt, with clues to go to each place and try to spot something in particular.
As for soccer, I wasn't sure about the fields so I asked other moms here in Florence if they could offer some suggestions (I have a 5 month old so haven't gotten to that point yet

). I was given some suggestions as well as told that it just isn't possible, unfortunately. I found out that the soccer fields are closed off to the public, only sports clubs with kids covered with insurance and proper certificates from their family doctor can go in and play on them, following very strict schedules as to who is on the field on certain times. It makes sense, I suppose, since soccer is so popular here... one place I called to ask said they have over 400 kids!! And that they can't open it to the public for that reason...
The best alternative is to bring a ball along (or buy one here) and head to the park to kick the ball around and burn off some energy. There are two big ones but not within the historical center, you'll need to head either to Le Cascine (there is a big green field to the side of the Piazzale J.F. Kennedy) or to Albereta, off Piazza Ravenna.
Both are parks that run along the Arno river but on opposite ends of Florence, so depending on where you stay one will be closer/easier to reach.
Hope I've helped offer some ideas, do let me know if you need some more!