This is just MY very personal opinion, and it is based on MY personal experience.
We went to the Bahamas in March. We stayed in the Cable Beach area. I was pretty unimpressed with that particular island. We have been here a few times in the past on cruises as well, and it's just a really overpriced tourist area.
I'm sure there are beautiful, less tourisy islands in the Bahamas chain, but Nassua is kind of trashy. And I personally looked into the Atlantis and found it to be extremely expensive.
On another note...I don't know if it was just at the resort we were staying at, but I have NEVER had worse customer service in my life. The staff was just plain rude. And it was just about everyone we encoutered. We thought that maybe it was just us, like we had done something to offend the staff in some way...but in riding the shuttle back to the airport and talking to other hotel guests we found that most of them experienced this same level of treatment.
It was bad enough that it ruined my impression of the country. I won't go back.
I think if you want to do a "beach vacation" with your family you may find that the Atlantis has all that you need. Be aware that it's truely an island. If you want to experience anything else, you will need to take a ferry.
Aruba is very nice, and St. John is beautiful! And the beaches in good ol' Florida are just wonderful too. Maybe you could look into a stay near Cocoa Beach, and get a beach and Disney vacation at once.
Good Luck!