> The same total work gets done by the same group of people in both cases, but the second measures as "better" for "the economy".

It's worse than that, because it's not the same work. In Scenario B the person watching the kids isn't their parent so they don't have the same bond or interest in the child's long-term success. It also introduces a lot of additional inefficiencies because now you have trust and vetting issues, either the child or the person watching the child has to commute every day so that they're in the same place because they no longer live in the same house as each other, etc.