Besides not giving the ages of your children/people in your party, you don't say where you are staying--onsite or offsite. Disney onsite usually says 4 plus one child under 3 (infant). But some hotels offer you more people per room. The Contemporary, The Polynesian, The Grand Floridian, Beach Club, Yacht Club, Animal Kingdom Lodge (depending on room), Fort Wilderness Cabins, & Disney Vacation Club 1 bedroom properties (see about renting points) all offer 5 guests if you are onsite. You can also just go for two connecting rooms at a value resort. Can't really help you off site, since having children we no longer stay offsite.
Basically, if your kiddos are older, you'll have to switch hotels, get two connecting rooms, or go to a condo type property. Unfortunately, you can't change hotel policy, just have to work within it.