mboy, I suspect you need to review your grasp of probability.
The subtley lies in that the children are not the same child.
By the question “is at least one of them a girl”, you allow for the chance that this could refer to either of them. We aren’t dealing with probability of future events, as in your coin toss example, but of a predefined existing situation.
If we only knew that she had 2 children, we’d have the following possibilities:
Boy/Girl
Boy/Boy
Girl/Boy
Girl/Girl
As we know that at least one is a girl, it rules out the Boy/Boy scenario.
Of the scenarios we have left, two involve one boy, and one girl. Resulting in a chance of 2 thirds.