Hi Kelly,
For bunk beds, you'll need to look at Animal Kingdom Lodge, Wilderness Lodge or Fort Wilderness.
Animal Kingdom and Wilderness Lodges will be one hotel room with a small "dorm-size" fridge.
The option that seems to suit your family's needs would be the
cabins at Fort Wilderness. There's a separate bedroom with a double bed and bunk beds, along with a murphy bed and sofa in the living room. A full kitchen would give you space for groceries as well as to have elbow-room for meal preparations. There's even a charcoal grill outside!
The cabins are considered a moderately priced (for WDW!) accommodation and Fort Wilderness is a fun resort.
Another suggestion would be the All-Star Family Music resort where there are
Family suites. A separate bedroom has a queen size bed, the living room has a Double-size sleeper, convertible sleeper chair, and 1 convertible sleeper ottoman. There are 2 bathrooms plus a small kitchenette area.
There are more resort designed to give families extra bedding options, review them
here. Often, it can be less expensive to get two rooms at a value resort than book a cabin, family suite or villa.
Make sure to stay on top of Special Offers to get your greatest savings! Watch for them online!