Hello Rebecca,
What a great dilemma you have on your hands. If I were to toss the Pixie Dust up in the air, here's how it all would land.
The
Yacht and
Beach Club Resorts are sister hotels and share many of the same amenities. The pool is awesome and your family will love it. It's a shipwreck with a sandy bottom. And their location is perfect. You can walk to Epcot and Hollywood Studios. And you're on the BoardWalk so there's tons to do for the kids even when you're not in the parks. Choosing between Yacht Club and Beach Club really comes down to a matter of preference of room themes. I personally prefer YC.
But there's something special about the
Polynesian Resort. It has its own Monorail so you can easily get to Magic Kingdom and Epcot. There are tiki torches, a pool with a cool volcano, and you can watch the Electrical Water Pageant at night its beach. But coming from California, I'm not sure how often you get to Hawaii. I ask only because for some people, including my sister who lived in Honolulu for several years, a stay at the Polynesian loses its appeal. Just something to keep in mind while planning.
Hope this helps. Enjoy your trip!