Responses
Also, to elaborate on your comment, 'big brother' can be spoken to any male older than you that you are 'close' with (she's a kid so she's speaking in a cute way) and doesn't have to be family at all, which is why cousin was saying it to Yuyang
I'm posting this as a separate comment for those who are confused about the whole sister thing:
In China, cousins are considered like sisters and brothers too, and their children are considered nephews and nieces (this is true in many Asian countries). It's clear from the family pictures we've seen of Lihuan's family that he's an only child and that the little girl is a relative such that it's easiest to call her a niece (my roommate is from China, and she calls her cousin's son her nephew). Chinese people would understand this, but other people wouldn't, so I don't understand why the translators translated without context. Maybe they didn't know either, since 外甥女 literally translates to sister's daughter, they probably didn't think to find out the cultural meaning of the word.