We have 5 kids which is one of the main reasons why we bought into the Disney Vacation Club. We use our points to stay in a 2 bedroom villa which gives us TONS of space - the master bedroom has a King bed, the 2nd bedrooms has 2 Queen beds and the living room has a pullout sofa and a pullout chair. The villas also have a washer/dryer and a full kitchen.
You can rent points from a DVC member and save quite a bit of money vs paying Disney directly for the same room.
You can also stay at the Family Suites at the All Stars or the Fort Wilderness cabins or just get 2 adjoining rooms at Pop or one of the other resorts.
We always eat breakfast in the room (cereal and milk, pop-tarts, fruit, etc...) and then pack a cooler bag with drinks and throw some portable snacks (cookies, gummies, chips) in the backpack. Sometimes we get the
Disney Dining Plan which saves us money on the buffet meals for all the kids that are age 9 and under (right now that applies to all 3 of our boys).
We are lucky enough to be able to get the tickets using the military promotions or get annual passes with our DVC discount. If you are a AAA member then you can look into getting discount tickets that way as well.
We set a budget for souvenirs and each child can pick out something within that budget (usually $25 to $50 per child).
We pay cash for our trips and use money from ebay, yard sales, consignment sales, craigslist sales and any per diem that DH gets from going TDY.
You don't have to spend a TON to go to Walt Disney World. The kids will have a blast just being there. Don't worry about being sucked into having to do all the "extras" like character meals every night, Bibbidi Bobbity Boutique or pirate cruises. While those are great fun, they do add up and when you have more than 1 kid then it gets very pricey.