I haven't read the whole thread here so I am sorry if someone else already suggested this. Depending on where you live, you might look into flying out of a different airport. I am about the same drive from two major airports and can pick and choose based on price (and they can be drastically different). I would exhaust every option. I don't know how your kids do, but my 3 & 4 year old don't last 3 hours in a car...forget about a plane. I have no desire to spend that much time on a plane with little ones...and no desire to deal with layovers either. I am willing to pay more for keeping them happy.
That said...make sure you look at all options. Try some different sites for booking flights with a discount. Look for groupon deals (doubtful, but worth looking at). Make sure you look into pricing for luggage and such as well. Make sure you find all hidden costs while booking flights...sometimes the cheapest isn't the best. (I've haven't flown JetBlue in years so I'm not sure how they rate these days). If someone is dropping you off and picking you up...and you live close enough to two different airports, see if it is cheaper to buy two sets of one way tickets vs. round trip.
