I add my voice to the choir. November is a good time to go. Yes, the days will be short, but with 6 kids in tow, 6-8 hours of intensive sightseeing is likely to be about the maximum you can expect anyway. Get everyone up and out early, have short daytime breaks - no long lunches - and then relax. Lines won't be long, if there are any, so you'll have more daytime sightseeing hours. Gelato is available all winter. Cities don't close down at sunset either. Some museums have evening hours at least once or twice a week and you'll be able to enjoy the beautiful centuries-old buildings illuminated - something that many tourists miss because of the long, long days at other times of the year. Be prepared for some rain, but it would be odd if you didn't have at least some warm (60s or more) sunny days over a week and a half.
3 stops is good for what sounds like 11 full days on the ground. You can day trip to Siena by bus from Florence - go on a sunny day. Pompeii is a very long day trip from Rome, but it is doable. Consider going to Ostia Antica instead - it's the ancient port of Rome and also 2000 years old and well-preserved. You can do it as a half-day trip from Rome. Assisi takes to long to get to from anywhere, so it's not a good day trip. Another hill town, Orvieto, is well worth it, though, and there are fast trains from Rome.