OK maybe livid is a bit strong, but I certainly wouldn't be happy. I just fail to see why people feel the need to interact with kids who are doing their own thing, thereby upsetting them and making extra work for their parents.
I think that anyone who thinks it's OK to pick up someone's baby and swing them round has only ever had sociable kids who don't mind that sort of thing. DS1 is shy, and hates that kind of uninvited interaction. It would upset him and make him want to go home. Yes it's a pain and yes it's his (and my) problem, but I'm fed up of having to apologise to adults for his lack of positive response to their behaviour, when really I just wish they'd minded their own business in the first place!
And before anyone says it's my fault - I've always been very sociable myself, and "socialised" my kids from an early age. But kids are what they are.
For what it's worth I wouldn't have been as frank as OP, and would have muttered my usual apologies about DS being nervous of strangers, but it doesn't mean I wouldn't have been cross that the woman had felt the need to interrupt my child and upset him.
And LeeCoakley - nasty little sarcastic post - of course smiling at my kids wouldn't make them cry, when did I say that?
But please, someone explain to me why a child should be interrupted when they're playing, and swung around by a stranger? What possible explanation is there for this?