Howdy Amanda!
I would recommend that you consider one of the Deluxe Villas. By staying in one of the
Disney Vacation Club Resorts, you will be able to experience the magic of Disney combined with many of the comforts of home. The 1-Bedroom Villas (and larger) have a kitchen and full size washer and dryer, which are both very helpful when travelling with small children.
While any of the Disney Vacation Club Resorts would be great, I would suggest
Bay Lake Tower at Disney's Contemporary Resort.
Bay Lake is conveniently located within walking distance to Magic Kingdom. The pools are wonderful and there is a white-sand beach your kiddos might enjoy. Chef Mickey's is a great character dining experience located in the Contemporary and you can always hop on the monorail and enjoy a ride over to Epcot.
The Contemporary Resort Campfire is a great way to wrap up your evening and your will love spending some time at the Community Hall where they can play games or do crafts. The Cast Members in the Community Hall are wonderful and will help you find all kinds of age appropriate activities to entertain and delight your kiddos.
Bay Lake is wonderful and I think it would be a perfect choice for you and your family!
Thanks so much for your question and please let me know if you need any further information as you plan your vacation. Have a magical day!