Unfortunately, there is no such thing as an inexpensive WDW vacation, nor are they any secrets to saving big money. What you need to remember, is that throughout your trip, you have choices, and that little expenses can easily fatten up what's already going to be an expensive vacation. My biggest suggestion is to create a spreadsheet and map out costs; the better your spreadsheet skills, the better the information will be. It will also help you understand how each of your choices are interrelated.
For example, if Southwest Airlines charges $125 more than an airline that permits only a full-sized carry-on, that means you're paying $500 in de facto baggage fees on Southwest, NOT "for only $125 more per person, I can bring extra bags on Southwest!" Remember... you can pack light, and pay just $120 round-trip (not $500) for two check bags... or many even nothing. Walmart sells a lot of what you don't bring for cheap, whether it's $1 for six quality toothbrushes, or $2 for a kid's t-shirt that's perfect for a couple days in the hot Florida sun (then disposed of/donated), or $1 for a pair of Tide pods... $50 can easily save you $450. And if either you, your spouse or one of your kids simply cannot live without bringing three outfits per day + extras... now's a time to have a good talk about it.
And remember... there's other transportation options, including driving, taking the Greyhound or even Amtrak (which currently has a BOGO sale going on for the next few days, if you live near a stop on the two trains servicing Orlando - note the AutoTrain is excluded). Perhaps a combination of both -- rental car companies often offer $1 rentals to take the car from Orlando, for example. And Greyhound often has sales where a family of four can travel for $200-$250 total, including one checked bag per person. Always consider all costs -- if you can't get by without bringing a ton of bags, and you live within ~1,300 driving miles, a car may be best for you.
Like I said, decisions are interconnected. There are oodles of beautiful, timeshare resorts that you can rent a room in. And the laundry facilities (reducing checked bags) and kitchens can wind up saving you over $1K.
One last thing: buy tickets at home, especially during clearance sales. I saw a light-up Christmas necklace at Kohl's for $1, which would be perfect to wear at Disney during December. I also saw a Mickey Mouse waffle maker for $7, which would be perfect for making morning waffles (and can be re-used). I've seen plenty of Disney coloring and activity books at Walmart for as little as a quarter. There were tons of little girls Disney princess outfits for $2-$5 (marked down from as much as $20). All of these are inexpensive ideas of similar items to bring with you. NEVER give in to temptation at Disney. Whether it's snacks, treats or souvenirs... these things are overpriced and add up really quickly.... and the truth is - none are necessary.
Playing off the idea: NEVER give in to temptation. If you're on a budget, stick with it! It's so easy to get carried away, you have to learn to tell not only your kids no, but yourselves as well.