I'm biased towards Maui, too, but the world is a big place so I'd vote for expanding your horizons. If your kids are okay with sitting in a car for a long time, I'd opt for Big Island because there are more places of interest on BI, esp the active volcano. Surely that's something they'll remember for years to come. I'd go there first so that you'll end your vacation someplace that feels like a second home.
I've never been to Kauai, but I picture it being like St. John. The geography is beautiful and great if you are a "seek your own adventure" kind of family, but there's not a lot of touristy things to do. If your kids would be content hiking, snorkeling, and cold chilling then I'd consider this as a viable option. If they wouldn't then I'd opt for BI.