As someone who has imitated every show I can for a Family Night, I personally would not touch "American Idol" with a ten foot pole. Too much variability with not enough variables under my control.
First of all you are dependent upon cute kids doing karaoke. Sounds great in theory, but we have been at enough campgrounds that hold karaoke nights and kids doing karaoke gets old mighty fast. Too many kids either start laughing or just barely sing.
Second, our metropolitan school district does a district wide "Variety Show", open to 10 elementary, 3 middle and 2 high schools and the talent is there to hold one show, but if it was just our elementary school the "talent" is pretty thin. Or I should say the "talent" that people would come to see and be entertained is just too thin in an elementray school. My daughters are in dance and I love their recitals, but to watch just one or two kids do the dance by themselves and it gets pretty old also.
Just my opinion. I just like to have everything under my control when I do a Family Fun Night, and this is just too much variability.
However, if you come up with a neat way to pull it off I am willing to give it a try. Always up for something new.