I'll second the Alta kids' ski school -- my daughter has had about 6 group lessons there, mostly with different instructors, over the course of two visits two years apart, and she's liked them all (including the instructors, who seemed like a cool bunch of dudes -- last visit they were all guys).
She's also had great experiences at Snowbasin and Solitude, also in Utah, and at Revelstoke in Canada.
I will add a caveat though -- all of these lessons were taken outside normal US/Canadian holidays, and the groups usually numbered no more than three. Quite often she was the only pupil. I think this was a big factor in their success -- as the youngest of her siblings by a long way, she has been virtually raised as an only child and thus relates fairly well to adults. So it's a big treat for her to have a grown-up instructor all to herself, and it must simplify their job too.
I'd also point out that Snowbasin and Solitude (and numerous others too, no doubt) are well off the radar for most Australian/NZ skiers, so outside US holidays and weekends, their ski schools really don't get a lot of business. And Revelstoke doesn't get a lot of families (or even that many women, when we went there four years ago), so ditto there for kids' ski school. Only drawback would be if your kids prefer the social or even competitive aspect of being in a bigger group and don't care so much about the amount of individual instruction they get.