"What proportion of two-children families with a boy born on Tuesday have girls?" seems completely clear to me. I would have answered that question relatively quickly.

But the original question had me very confused. I felt a strong desire to ask more about the situation. A great deal of my intuition wanted to say that "well there is nothing special about Tuesday... Any boy that he has is going to be born on some day of the week, and if whatever day of the week that son is born on is included as this line item in the question, then that line item is irrelevant."

I wouldn't have fallen into that same trap in the case of the "What proportion of two-children families..." version because the "Any boy that he has is going to be born on some day of the week" logic doesn't apply.

Tuesday seemed like it might have been arbitrary in the original question, where it seems explicit in your rephrased version.