Totally depends on what time you're going and on what day BUT I've been on it loads of times and never had to wait more than 10-15 minutes for what that's worth. Often you're on pretty much immediately as so many people can fit in each car, I tend to try and go at dusk though, so if you're trying to get on in the middle of the day, it will be worse, unfortunately it's a YMMV situation.
Are you coming by rail? I think the eye is on the 2 for 1 if you are, worth checking anyway.
What sort of things are your kids in to? It depends on what you want to do with them really, the exhibition road museums are normally packed, but you can do stuff like take canal boat rides which are normally much less busy and more interesting (and stop off to go to the zoo if wanted).
I can suggest some alternative museums if you'd like, but with kids that young I don't know if they'd be interested in semi-scientific paraphernalia or the museum of brands or bodyparts, my taste in museums runs quite eclectic
But maybe the -
http://www.horniman.ac.uk/ or I've never been but heard good things about -
http://www.vam.ac.uk/moc/index.htmlI really like Kew bridge steam museum, so much that I'm thinking of volunteering to become a train driver -
http://www.kbsm.org/Everything on the south bank is always totally rammed
but there's some nice city farms I suppose, if that's of interest like
http://www.batterseapark.org/ or
http://www.wwt.org.uk/visit-us/london