The rooms are in the process of being refurbished at the Swan. If you can get an updated room, I would definitely stay there, as the new rooms are very nice; the Dolphin rooms will be redone, following completion of the Swan's renovation.
The Swan is a smaller resort than the Dolphin; that may mean less chance of getting a room with a balcony.
The Swan and Dolphin share facilities with one another, so that means your kids could use the great pool area and Camp Dolphin at the Dolphin Resort, no matter which resort you are staying at.
http://www.swandolphin.com/kids/index.html
If you have elite status with SPG, I would suggest calling the resort, after doing your award booking, and placing your special request for balcony, remodeled room, view, etc., directly with them.
Reservations (direct for Swan/Dolphin) 888-828-8850
Both resorts offer excellent location and very good facilities - especially with a points booking.