I agree with the Accademia and the Uffizi, with the Bargello as a backup if the Uffizi sounds too tiring.
The Accademia, with Michelangelo's David sculpture, is small and can be visited in an hour. It's fun to watch the people watching David -- it's almost as much a social scene as an art museum, so it's hard to get bored there.
The Uffizi is the best painting museum in all of Italy, I think. Incredibly beautiful works of art. But it is large, dim in some rooms, and the lines can be really frustrating. If you love Italian painting, it's still a must. If you prefer sculpture, or if two hours of shuffling crowds sounds like it would send your daughter over the edge, then the Bargello is a good backup choice. It is an all-sculpture museum with an open-air courtyard in the middle, so it's more refreshing than the Uffizi. We were in and out in an hour.
Also, just want to remind you that Rick has GREAT audio guides of many sights in Italy, including the Accademia and the Uffizi. They are available for free download off the website. His commentary is fun and holds your attention, and you can listen to it on any mp3 player, thereby satisfying the iPod need. :-)
Have a wonderful time on your mother-daughter trip!