My adult children both love art museums and have since childhood. One reason is that when they were the age of yours our museum visits were always with them in mind, not death marching them through museums to see what we wanted to see. 6 hours of museuming with kids this age is a great way to help them grow up to hate art museums. I would spend an hour max at the Academia with David as my object. for the Uffizi, I would have the kids each pick out a few pictures they want to see on line or else each parent take one child and let them choose a picture to look at in each room and let them drive the bus. We love the Uffizi and usually spend about 4 hours on a visit; there is a coffee shop where we have had gelato on the terrace; It is now pricier and requires heftier purchases to sit on the terrace than when we began -- but it is one way to factor in a break and treat for kids at the Uffizi. There are wonderful things at the Uffizi but I would focus on helping the kids choose a handful to see.
I would also not climb two arduous towers; the Duomo is historically and architecturally interesting from the inside -- I'd be inclined to choose that one and study up a bit with the kids about the creation of the dome before tackling it. I would imagine it might be a bit daunting for the 6 year old to make this climb.
Florence has several good gelato places (and several mediocre ones, usually with great heaps of gelato topped with colorful fruit slices along tourist tracks) Maybe make finding the best gelato a family activity. Some suggested spots to try: Vivoli not far from Santa Croce square, Perche Non near Piazza Signoria, Caribe near Academia (they specialize in granita). When we traveled with our daughter at 10, the hunt for great gelato was a fun part of the trip.
Palazo Davinzati is a restored (over-restored) Renaissance home which might be interesting to the kids; the Musee San Marco is a monastery where Fra Angelico painted devotional frescoes in the cells of the monks. Both are small sites easily visited in an hour or less.