Private Affair is a private dinner where the chef prepares a meal just for your party. It's $150 for 1-3 people, and $50/person for 4 or more. It's held at Signals, which is one end of the Beach House building. The tv room is in another section, with is not visible from Signals (you can't keep an eye on your kids if you're inside Signals and they're watching tv). Since the Beach House is open to all guests, it is possible anyone can be wandering through there, and although I'm not generally a nervous parent I don't think it's a good idea to leave a 5 & 7 year old alone in there. Most likely nothing would happen, but why take the risk of an abduction or other problem - or the kids could just plain get into trouble with horseplay of their own and get hurt. There is no childcare center like at the wdw resorts, so the childcare is the responsibility of the parent - not the resort. They may have a babysitting service they could recommend, though, if there's not a structured kids' activity that will cover the entire time of the Private Affair.
We're doing ours on March 18th, but since the only kids with us will be 16 & 17 we don't worry about childcare <g>. We'll just give them money to go out for a pizza or get burgers at Fuddruckers, while the 4 adults enjoy the Private Affair.