Responses
From what I can put together, I'm guessing one of Ayumi's parents is either siblings with, or first cousins with Kotaro's mum. When Kotaro refers to Ayumi as "my relative's brother" I think it's brother in the Japanese way (as in they call male cousins 'brother' even if they aren't actual siblings).
You are totally right in that the uncle tag is inaccurate. If Ayumi was actually Kotaro's uncle, that would make Ayumi's parents Kotaro's grandparents (which was not the case). I mean yes they are still related, but it's not uncle/nephew. the Uncle tag is misleading.
needs to leave.
Nowhere in this story does it specify which sort of relation Ayumi is to Kotaro. I personally think he's something like a second or third cousin, but definitely not uncle. The only uncle mentioned in this is the one they attended the funeral for.