Here is my take. I don't think there are many, if any, direct flights to Orlando out of the Bay Area. And direct is always the best option for flying with multiple kids. Less schleping your carryons, stroller, carseats and kids through the airport.
SWA has the most flights through Oakland or San Jose, and either of those would be easiest for you. Sacramento (SMF) is a smaller airport also, and I don't think they have many off airport parking lots to use, so parking may be an issue if you don't have anyone to drop you off.
SWA can also be pretty cheap if you are able to plan ahead and watch for their sale prices. Plus they give you free checked bags, so that is a savings over the other airlines. Carseats and strollers fly free on most all airlines.
Overall, I think flying is a great idea, vs driving both directions. You will get so much more time in Orlando, for really not much more money. Flights will probably be $400 or so each, so $2000 for the 5 of you. The kids are still young enough, that they wouldn't get too much out of a x-country trip, even if you did want to make some stops.