Family vs Relatives

It's easy to know who our Relatives are - those persons who happen to share a close common genetic background and therefore ties of blood and bone and cell structure at the most fundamental levels of DNA.

Defining who our Family is, as opposed to those who are relatives, is not always such an easy or clearly defined task.  Relatives, after all, are a trick played by fate.  You have no choice about who happens to share common ancestors with you, whether you like them or hate them or could care less one way or the other.  It doesn't even matter whether you've even Met them - they're your relatives by a quirk of fate and not through any effort on their part nor great goodness of their spirit or conduct.

My relatives, without exception, are NOT considered part of my Family.  While I may have no choice about whether I share common ancestry, genetics, or DNA with these people, I DO have a choice as to whether I'm going to associate with them, pay attention to their opinions, care about them in the slightest, or respect their existence.

The question happened to cross my mind recently, while considering the whole "who is my family" issue:  Is it possible for me to consider someone part of my family while they do not consider me part of their family?  Is it possible for me to maintain the loyalty and caring of family towards someone who indicates to me - either by direct words, or by their actions, that they consider me inadequate - not good enough - to be part of their family?

It's something I haven't, yet, been able to answer for myself.  But I will no doubt find some resolution before I set the question aside completely.  I have to, for my own peace of mind.