WWII era Japan was surprisingly progressive, it seems
A slightly more likely option is that they got back together after their husbands died(a prerequisite for having kids in the pre-modern era, which is a prerequisite for grandchildren by definition), having stayed close enough the entire time that their kids ended up marrying each other. So the kid could easily be thinking maternal vs paternal grandmother, without necessarily realizing what's going on.
Sorry to throw a cold bucket of water around, but my analysis switch got flipped.