For our family, its the Beach Club, particulary since we only go over the summer. Stormalong Bay is simply amazing!!!! We love the resort: the whole vibe, the location (seriously, it took us under 5 minutes to walk to Epcot!!!), even the smell when you walk into the lobby. It's our new family favorite.
But with kids the ages of yours, you'll be spending a lot of time in the Magic Kingdom. So allow me to put in a plug for the Poly.
It's lush and gorgeous.... it really does transport you to a different place. My kids loved the volcano pool with its waterfall and zero entry. And the location is also wonderful-- the monorail to the MK is right there, and you can walk to the TTC for the Epcot monorail. (I really had to talk my kids,particularly my son, into the Beach Club last year. The monorail has always been one of his favorite things about WDW.) For young kids, it really is a wonderful choice. My girls learned how to do the hula one year, and there's almost always someone in the lobby doing coloring pages or a craft. And you're a short monorail ride away from the Magic Kingdom... that's incredibly nice at the end of a long day!!!!
I agree with the poster who said that it might be hard keeping track of 3 young kids at SAB. It's immense; there's no one spot where you could sit and see everyone in the water. Yes, there are lifeguards, but I always figure they're the backup, not the main source of safety. The Volcano pool at the Poly is different; unless they're up on the line for the slide, you can see them.
Really consider the Poly, it's a wonderful choice! I would think that it's probably the best choice for your family.