Maybe this is because English is my first language - but I cannot imagine how "I have two children, and one of them is a girl" could mean: "I have two children, and the gender of one of them is #{my_first_child.gender}." - if someone was to confer that meaning I would expect him to say: "I have two children, and the gender of my first child is girl". But frankly as someone already pointed out - normally the sentence "I have two children, and one of them is a girl" would implicitely mean that the other child is a boy.
It's the difference between the situation where a child is chosen and then the gender announced, and the situation where a girl is found, and then the gender announced. If you started out saying "Is one of them a girl?", and only continuing if the answer is yes, then the probability changes.
