I think that the skill would be more useful if there were multiple concrete actions underneath it, and then a broad penumbra that extended out from them, to help players conceptualise when they want to ask to roll it.
The writeup below is the first one of those concrete actions, which I wrote for use in the Dawnlands by Kadiz nomads and Hill People (cannibal elves, mainly).
The custom on the plains is that two people with a nameable common ancestor are considered related, with further degrees of relation being less important than nearer ones. However, even distant relatives must be shown and in turn must obey guest-right, which spares them from violence to their person and property and binds them against the same. Therefore, when not openly hostile (i.e. on a raid), the first thing two bands of travellers do when they encounter one another, whether Hill People or Kadiz, is begin shouting out the names of their relatives from a safe distance.
While the lack of a common ancestor does not automatically make either party hostile, it does mean that either side is free to use force if they wish. The complex kinship web on the plains means that almost everyone, Hill Person and Kadiz alike, is related somehow if the two sides are adequately informed about their own genealogy. Note that merely because the ancestor was kidnapped or owned as a slave by the other side does not normally absolve one of guest-right.
An ordinary success means that the PC or NPC has identified a common, but distant ancestor by which they and their target are related.
A critical success means that the PC or NPC has identified a common, near ancestor they share (sister, brother, son, daughter, father, mother, uncle, aunt, first-degree cousin, wife, husband, concubine, catamite).
A failure means that no common ancestor can be identified.
A critical failure means that something about the genealogy gives offense to the other party, usually turning them hostile. This might be naming a hated foe as one's relative, or establishing a relation that is particularly embarrassing to the other party (A man's catamite is considered a close relation, but saying that someone's ancestor served as your ancestor's catamite is deeply shameful) or that casts unseemly aspersions about the other party's lineage (specifically adulterous relationships and sometimes bastardry).
This can be an opposed roll if one side is attempting to shirk guest-right. They downplay the relation, or present it as illegitimate or claim it as false.