You're over-complicating things.

For each person (the man and the woman), there are four possible outcomes of equal likelihood.

In the man's case, we already know the first child is a boy, so we only consider that branch. There is a 1:2 chance of having another boy, and thus a 1:2 chance of having two boys in total.

In the woman's case, the only outcome we know will not happen is girl-girl. Taking that out, we're left with three outcomes of totally equal likelihood, and only one of those is boy-boy, thus she has a 1:3 chance of having two boys.

Jibb