Hello Michelle! You actually have lots of options. I'm not sure what your budget is so I'll provide some ideas at both ends in terms of cost.
On the higher end, in terms of cost, you could stay in a 1 or 2 bedroom villa.
Villas are convenient because they offer some of the luxuries you would find at home - a kitchen, living area, etc. There are many villas available across the Walt Disney World resort and you do not need to be a vacation member to book a room.
On the lower end, again - in terms of cost, would be a
family suite at All Star Music. The suites include a convenient layout with a separate bedroom (with a queen size bed) and a living area with pull out furniture. There is also a small kitchenette and two full bathrooms.
In between the above two options, you may want to consider a
cabin at Fort Wilderness. As you can see from the pictures on this link, there is plenty of space for a family and it accommodates up to six people.
At if you are looking for two adjoining rooms, this is an option at any resort. Often when my children were smaller, we would opt to get two bedrooms at All Stars (this is before the suites were available). It was convenient when the kids would fall asleep at different times and we were able to stay in a separate room.
I hope this helps give you some ideas. If you have any follow-up questions, please let us know! Diane