There's a lot of confounding variables here. Divorce could be a symptom of an underlying cause which could be the actual reason why kids do worse. Or it could be that when people pool their resources, it creates a more stable home (in resources and labor) and stable homes are a stronger cause.

Re:stable homes, it'd be interesting to envision whether non-nuclear family structures would be more stable. Maybe matrilineal/ matrilocal cultures (even if they're patriarchal) where children of a family are those born to it's women (more stable family since you don't divorce your siblings/mom, much freer relationships, paternity maybe unknown etc). The book Sex a At Dawn (controversial book!) explores these ideas.