Hi, Jennifer!
I think you are absolutely right to be looking into either
Polynesian or the Beach Club. Between the two, I would lean toward the Polynesian. With younger kids, you will probably be spending a majority of your time at the Magic Kingdom which is just a quick monorail ride away from this tropical resort.
From the Polynesian, you can also take a lovely stroll through your resort to the Transportation and Ticket Center where you can catch a monorail that goes directly to Epcot. Very convenient! Bus transportation is available to Hollywood Studios, Animal Kingdom, Downtown Disney, and water parks.
Other features of the Polynesian that I think you will enjoy include a great beach with views of Cinderella Castle (perfect for viewing fireworks) and a wonderful swimming pool with zero-depth entry. We also like the food court area, Captain Cooks. We enjoy getting our breakfast from there and sitting pool side in the mornings.
We usually get a garden view room, and request a building near the Great Ceremonial House (the main building.) When our kids were little, we also requested a first floor room so we didn't have to worry about elevators with strollers, back packs, and diaper bags to carry!
I hope this resort is what you are looking for! If not, or if you have any other questions,
let me know!