If you are flexible, Disney can be affordable. With a large family you may need two rooms at one of the All-Star Hotels or the Pop Century. If your family can fit into one of the family suites in the Disney All-Star Music, you may only need one room. The Old Key West Resort also has a lower priced room that has a separate bedroom, fold out couch and bed that drops down from the wall. Fort Wilderness Campground also has cabins which are more friendly on your wallet then some of Disney's hotel options that have large suites. If booking online, be sure to unselect the preferred room price to save some $$.
If you are willing to go at their lower visited seasons the price drops too, but school vacations do not fall under their lower rates.
You can try the hotels just outside of Disney too, but staying at one of the Disney Resorts is the better value (at least to me, see hub for why...)
Also, when choosing a park ticket, I think it is worth the extra money to do the park-hopper option. Say you are visiting Animal Kingdom which closes earlier then the other parks, you could still go to Epcot at night for the fireworks! Make sure to select the amount of days you need the ticket for, if you are staying seven nights, but your flights barely let you have time, see if the extra cost between the 6, 7 or 8 day ticket is worth the time you have on you arrival or departure days.
If you are flying, and didn't book early enough, try flying from a weekday to a weekday.
Additionally, they do have a promotion they are extending longer then other years in the past that gives you some free meals. It is only for certain times, but it will save you the cost of 2 quick-service meals a day plus a snack.
Hope this helps!