I have examples of all the types of photo mentioned here and in Bjorke's blog post - including one taken by my wife of a laughing baby and a vomit-covered father. It's impossible to give tips (even cynical ones) until you know the reason for pushing the shutter, even if that reason is unspoken.
I love most the photos that show what I imagine to be my childrens' inner life, although from the glimpses of that life revealed by what they say my photographs are more about my lack of imagination than their wildly lateral way of thinking. I prefer the everyday miracles to the groomed portrait - however intense - but on the other hand, I am not unaware of the interconnection between spousal acceptance of gear lust and the production of cliched shots of the kids looking cute.
I think it is somewhere in the Winogrand interview that is currently all over the blogs that he makes the point that family snapshots are the most staged photos of all. I think this is doubly true once the snapshots are edited for inclusion in an album or display on the wall.
For me, the best tool to get children to behave is a well-placed grandmother. The only thing that beats it is a well-placed grandmother with a digital camera.