Hi Megan,
In my opinion, the Deluxe Villas at
Kidani Village, part of the Animal Kingdom Lodge complex (which consists of Jambo House and Kidani Village), have the next best pool and interactive water play area on property! It is fabulous. I am sure your children will love it! Since they are Deluxe Villas, they will have 1 and 2 bedroom rooms there. You can get a room with or without a Savannah view, though there's something magical about waking up and seeing animals right outside your room. However, the bus ride between the Magic Kingdom and the Animal Kingdom Lodge can be a little long; I would plan on it taking 45 minutes.
Another option would be to get a 1 bedroom or 2 bedroom Deluxe Villa at the Villas at the Wilderness Lodge, the Disney Vacation Club portion of the lodge. The pool area is very nice, though not as themed as Kidani's Village pool and there is no Uwanja Camp water play area, but my children, ages 5 and 10, have always enjoyed the pool at the Wilderness Lodge. I recommend this resort because the Magic Kingdom is only a boat ride away. The boat runs very often and I find the trip to be very relaxing and enjoyable, especially at night. There's also a separate boat that makes a circle stopping at the Contemporary Resort, Fort Wilderness, and the Wilderness Lodge; that makes it easy to get to the other monorail resorts for a visit via the Contemporary.
Finally, since you were considering the Beach and Yacht Clubs, you might also consider the Boardwalk. It is across Crescent Lake from the Beach and Yacht Clubs. The pool there is nice, though not as nice as Stormalong Bay or Samawati Springs Pool at the Animal Kingdom Lodge. However, if you liked the location of the Beach Club then the Boardwalk location is not that much different.
Good luck!