Alaska usually does "Kids fly free" in the late winter and spring. We did it last March for spring break. I realized later, though, that in most cases they charge you a full-fare price, and it can easily work out to be more than you would pay with a "hot deals" price for all of you. For example, DH and I had 2 of our kids fly free in our package, but we figured out that the cost of our two tickets was something like $1400. If we'd shopped around for the best deal into the least expensive airport, we could have gotten all four tickets for about $800.
Do try pricing out all your vacation components separately, airfare, hotel, and park hoppers, and see if you can't get a much better deal that way, before booking a package or a "free" special.