Hi and welcome!
Well, for starters, let me say that we've been saving for a year and a half for the trip we start in 11days! (I just had to work that part in!!!

)
As teachers, we go to WDW over the summer-- that one is non-negotiable. WDW has 'seasons" that don't match those of the real world. Our trips always take place in "Value Season" when resort rates are cheaper.
http://www.mousesavers.com/disneyresorts.html#offseason
Take a look at the pricing for the family suites at All Star Music-- they sleep 6. That's probably the cheapest you'll be able to do if you stay on property.
One of our biggest expenses is airfare from NY. I booked ours in January, and the 5 of us are flying to Orlando for $1320. Those exact same flights now run $2208.
Of course, if you're not flying and will have a car, you might want to consider staying offsite. Take a look at
www.allstarvacationrentals.com I've never used them, but they come highly recommended in a number of WDW books. Renting a condo/house also means you can cook your own meals, and save some money there.
One of the best kept secrets at Disney is the YES program:
http://www.disneyyouth.com/individual-enrollment/
What it boils down to is this: if even one of your kids takes a single 3 hour class, the entire family gets greatly reduced park tickets. All 3 of mine will be taking classes: my younger (with my husband chaperoning) will be taking Synergy in Science at Epcot. At the same time, my older 2 and I will be taking Making Waves with Marine Careers, also at Epcot. The 3 hours my family spends in what look like very interesting classes will save us something like $130 apiece on our 8 day parkhopper tickets!!! there are, of course, some things to be careful of: the YES tickets are non refundable and non transferable-- you have to be very sure that you're planning to use them before purchasing them.
Does that help at all?