Hi Justine!
My first thought was to suggest
Disney's Polynesian Village Resort, which is my second favorite Walt Disney World Resort just behind
Disney's Fort Wilderness Resort & Campground. We just got back from a stay there a couple of weeks ago and just love everything about it. The main draw is location, location, location! It's just a quick monorail or boat ride away from Magic Kingdom Park, which is usually where we spend most of our park days. It's also a short walk to the Transportation and Ticket Center where you can catch the Epcot monorail for a direct route to the park. The lava pool is fantastic if you're kids like to swim. BUT when I saw that you'll be visiting Epcot twice and Disney's Hollywood Studios once, my mind flipped to
Disney's Beach Club Resort, which is my third favorite Resort hotel.
From Disney's Beach Club Resort, you can walk right to Epcot's International Gateway entrance. There is also a pathway you can walk (about 20 minutes along the water) that will take you to Disney's Hollywood Studios. A ferry boat will also take you between Disney's Hollywood Studios and Epcot with a few Resort hotel stops in-between, including Disney's Beach Club Resort. A bus will take you to Magic Kingdom Park and Disney's Animal Kingdom Park. So this resort is also great for location, location, location! In my opinion, it is also home to the best Resort hotel pool, Stormalong Bay. It's like a miniature water park!
You can't go wrong with either of these options, really. Your family is going to fall in love with Disney no matter which one you choose.
Have a magical day!
Leslie