I once found my two cosied up in the owners bed!
He also ran into a bedroom and dived on the bed which unfortunately was loads of boxes stacked up with sheets and a duvet and fell apart
Neither of these would amuse me. Did the kids in the bed have their shoes on?
Our buyers brought their kids but had obviously decided who would be in charge of the kids, and who would be in charge of looking at certain details - they only wanted one viewing but it was a very in-depth one. The kids were pretty well behaved, especially given their ages, they were a bit young to understand about the cat, but they didn't chase her per se, just followed her around. It did end up with both kids, me, and the mum on our stomachs on the carpet looking under the sofa at the cat which was awkward given that I'd hastily shoved some stuff under there (nothing awful)!
I don't think there is anything wrong with taking children, but they need to be aware of what's expected of them and they need to be supervised, it's not fair to sellers otherwise, who will likely feel they have to put up with behaviour they might not ordinarily, for fear of losing a sale.