Sorry, but this does not make too much sense. At least not the circles and your conclusion.

If I see that right the first branching is for the first-born child and the second for the second-born.

In this case, the "boy"-case in the first branching has a chance of 100%, because we already know it's a boy. So we don't have to consider the "girl" case, because its propability is 0%. On the next-branching you have a 50%-chance that the second child is also a boy. You have to multiply it with the overall propability of this branching, which is, as I said 100%, so the resulting propability is 50%.

On the woman tree, we have at the first branching a propability of each 50%. If we follow the boy case, we have again a 50% propability for each case. So the propability of having two boys is 50%*50% = 25%.
If the first-born child is a girl, the propability is 0%, so we don't have to consider this branch. So the overall propability is 50%.

BUT WAIT!

We didn't consider that we know that one of the woman's children is a boy. So we should not talk about "first-born" and "second-born" children, but just "first" and "second" child, because it doesn't matter in which order they are born. Because the propability of the man having two boys doesn't change if we say that his second-born child is a boy and the first child's gender is uncertain, the propability doesn't change.
So, we can say the same thing about the woman's tree as we said about the man's tree, which will also result to 50%.

So the propability that he/she has two boys is 50% for each of them.