V funny thread in some respects, but I agree with Gray's point about it being an indication of female insecurity, which is a wee bit sad.
Or maybe I'm an underthinking, cognitively challenged individual, which is very possibly the case (despite the odd pg qualification, heavyweight yaddie yah and senior position, etc. 
). Because throughout all my children's toddlerhoods, this is never something I got worked up about. Indeed, I miss having the time and opportunity to chat to other mums that toddler years provide. I'd quite happily chatter, chatter, chatter too, as idly as you like (pity the synonym appears to have developed negative connotations as I always saw it as a fun word with a lighter, more amusing nuance), all day long.
I think our version had the Daddies nod, nod, nodding, which I always assumed meant they were either sagely agreeing with whatever the mummies were saying about the impact of 19th century Russian literature on the propensity of modern Russians to cut queues at ski resorts (or other such v idle chat) or nodding politely because they hadn't actually read the Russian literature but wanted to look interested (or as clever as the mummies).
I also have to admit that if the daddies were shushing, I would have assumed they were shushing the children. Because Daddies do shush children (quite a lot around here, but, in defence of the daddies, the children are rather noisy).
In my world, if the daddies shushed the mummies, the mummies would laugh at them.
We probably couldn't sing a version of the song with a verse that we felt was suggesting that because we'd be posl so much at the thought.
Does my sense of worth have to be validated by the words of a nursery rhyme? Or do I validate my sense of worth by how I hear the words?
Feck... Look at what you have me doing on a perfectly fine Saturday morning... [storms off to find a bus and someone to chatter with]