We went to Atlantis this November - sort of a forced choice because the other couple we were with was on a 10th anniversary trip and they got married there. I hated Atlantis a little bit less the second time, and I was underwhelmed by The Bahamas in general. We also did some nights at the One and Only and Sandals resorts and weren't really impressed with either of them for the cost, even at half-price through Expedia VIP.
If you are going to do Atlantis, the ONLY way to do it, IMHO, is to rent a timeshare at Harborside on the secondary market. We used redtimeshares(dot)com and were very happy with them, but there are other services/BBs. Try and get at least the premium 1BR if you have kids, the extra space and the full kitchen (as opposed to the half-kitchen in the 1 BR deluxe) is worth the small premium.
The full kitchen will save you hundreds of dollars in food costs (possibly thousands if you have teenagers), and even if you get tired of cooking, the Harborside marina - an easy walk - has a Quiznos for a reasonable (read $9 instead of $17+18% automatic gratuity) sandwich. Harborside has a daily grocery shuttle ($7 pp round trip) that takes you to a store like Whole Foods but with higher prices.
Or you can hire a taxi for $30 and he can take you to the SuperValu grocery store where locals shop. We packed a suitcase full of basic snacks, pantry staples like pasta and peanut butter, spices, coffee, dishwasher tabs, laundry detergent, paper plates, etc and only bought fresh produce, meats, and dairy while we were there. We even took a Brita pitcher so we could use refillable water bottles instead of buying cases of bottled water, but that was more a convenience/preference than a cost savings.
PM me if you decide to bite the bullet and go to the Bahamas, I have some other advice but don't want to ramble when I don't really recommend going in the first place.
ETA: Also how old are the kids? The other couple had a 2 and 3 year old, and they were too young for the Atlantis, they would have had just as much fun in any pool with a splash feature, although they did enjoy a few walks through the aquariums. The sweet spot would be older kids, say 8 - 13, they might really enjoy the water park and get value out of it.