Festivals vary. And they change over time. The difficulty is finding out which are the ones that fit your needs (and these vary over time too).
Some festivals do very well for children, though probably not that many. Of the ones I've been to, Sidmouth is the one that addresses the needs of children most satisfactorily, so far as I can see. They seem to have a whale of a time, crafts, games, and music and dance. The childrens programme often looks more interesting than that for the adults, with great performers involved. My y impressioin is that it turns out a lot of children who are folk-oriented for life.
Of course that's not much help to Mudcatters in America looking for where to go - but it's pretty clear that you've got some great child-friendly evwents over there too.
The problem with festivals is that, if they are successful they tend to grow bigger, and that can drive away the very qualities that make them enjoyable in then first place. I tend to prefer smaller festivals - but then they fold, because of lack of money, or the key people who do all the work move away or fold under the work-load.
The festivals I know which have managed to grow to a viable size without losing the qualities of intimacy and informality are headed by Fylde and Whitby. Sidmouth is too big, but has managed to run as a bunch of smaller festivals packaged together, so you can still get some of the small scale feeling.
Perhaps what people looking for the right festival should post a list of what that would mean for them (locality, type of activities wanted - eg workshops, dances, sessions - cost, children's festival etc) and then see if other 'Catters could advise from experience.
This could even be a standing facility, either a permathread, or a satellite operation like bbc's pages or the Mudcat Songbook. And I am not volunteering to run it. (Because that's what people always say when you suggest something - "that sounds interesting - why don't you do it"; it's what I always say too.)