I think Chinese and Korean culture share this concept, and I wouldn't be surprised if there were more Asian languages who did. Since a daughter joins her husband's family upon marriage, their children are considered belonging to the other family. I recently learner that apparently there's a saying in Korean that daughters always leave things at their mother's house when they get married so they have a reason to come back despite having left the family.

It refers to a male cousin that is NOT in the same paternal line, so maybe not too uncommon?

China, at least. Lots of distinction between mother side and father side. Grandma can be 老老 laolao (mother's mother) or 奶奶 nainai (father's mother), for example.