Translation:I like my family except for my uncle.
I do understand the distinction, however I think it is a matter of degree. I actually know someone who will say that he is going to visit his "relatives" even when he is referring to his brothers.
In my family, aunts, uncles, and cousins were "relatives". "Family" was reserved for siblings, parents, and grandparents (and now, thank God, children and grandchildren.) So my mother's brothers and sisters were HER "family", but MY "relatives".