I think you'll love it, it will be different than Disney, but still fun and their new rapid river ride is a blast, can't get anything like that at the Disney water parks!! It's a beautiful resort, the marine displays are interesting and with the addition of aquaventure there's more to do then there was a few years ago.
The bracelet you'll get will include beach towels, you get your bracelet at the towel station at Atlantis and then grab your towel.
There's a decent continental breakfast at CS each morning and there's also a Subway across the street.
I've been there once on a cruise stop and then we spent a couple nights there after a cruise a few years ago and we just grabbed a taxi at the airport but the guy was great, very friendly, gave us some facts and history along the way and we asked for his card so we could arrange to have him return us to the airport. I've hung on to his card in case I ever return (I can pm you his # if you're interested).
I think all the pools will be fine for your kids, if you're there for a week they'll be able to try them all.
Not sure I can help you much with excursions, the only excursion we've done in Nassau is with Stuart Cove, which was fantastic (third snorkel stop was with sharks, it was amazing, but exhilirating!!). I'm going on a cruise next March that stops in Nassau and this time we're going to Blue Lagoon Island, not sure yet if we'll do the dolphin swim though.
And I always thought if I went back for a longer land vacation I'd want to take the ferry to Harbour Island because I love island hopping whenever possible but I'm not sure what it costs to get there by ferry.
