Have you ever had a baby/toddler/child taken away?

Maybe?
It probably happened some of the first times I played with a family in the game. I do remember getting the warning, at least. It was probably triggered by having the baby in a cradle too far away from where the parents were in the house, which must have been quite big. I think I didn't notice the baby was crying (blue avatar).
But as far as I know I've not got that far with a toddler, since they are often more mobile and can take care of some of their own needs themselves.