Well your talking from a view of how (maybe) people see it, in England.
It's a very different structure, than other Countries.
People can be cut-off in England from family, say if they have done something to shame the family.(they then over time will become a distant relation).
I was born there, and left when nearly 10.
I know the thinking, and it's a very serious thing, family and all.
I would say to you it is in 2 veins.
1. where they have been made distant for some serious reason.
2.they have been made distant by lack of contact, say...Your Aunts - daughters husband....or...Your Mothers Uncle's daughter.
There is always a reason.....why...they are distant,
It is serious stuff too..
The reason I ask is because in the books/film of Paddington Bear, Mrs. Bird is a distant relation of Mrs. Brown, but they live together and are very close. That suggests it has to do with how closely related they are are rather than how close amicably.