The Comfort Suites package requires a two-night minimum stay. For two nights in August I found a room with two double beds for $176/night, but extra charges nearly doubled the nightly room rate. That said, once you figure in the sweeteners mainly the free Atlantis stuff, but also a few free meals for kids 12 and under you might find this is a good value, particularly when you compare your overall costs to a stay at the actual Atlantis which is running a $199 per night/three-night minimum special if you book by July 4th.
If you can convince your kids that a trip to Nassau would be complete without the Atlantis experience, the Sheraton Nassau Beach Resort is running a $229 per night/three-night minimum Love Your Family deal that includes a $50 resort credit per room, per night and reduced meal prices for kids 12 and under. The family will have use of three pools plus free access to such non-motorized water activities as sailing, kayaking, wind surfing, and snorkeling.