I suppose part of the issue here is how large and inclusive a Vulcan clan is. For what's it's worth, and relating somewhat to
Hando's pondering, I've interpreted a clan as rather large, with (traditionally) a small number of matriarchs serving as the spiritual and technical authorities - the supreme arbiters - who traditionally delegate political authority in more "mundane" matters of finance, administration, warfare, etc., to related males who then lead the smaller family units. Vulcan has been described in the novels as traditionally matriarchal, but the Vulcan nuclear family, and other smaller family units, have always seemed to me, both onscreen and in novels, to have a strongly patriarchal flavour. I tend to assume that a clan consists of multiple houses, whose leaders either official or unofficial are generally male, and who show in turn an allegiance to the clan matriarch(s) who has/have the final say in matters that affect multiple families or conflicts that arise between them.
I've always noted that the te-Vikram, the warrior culture in Surak's time mentioned/appearing in
Vulcan's Soul, etc., have all political leadership roles explicitly male, save one - the Old Mother of Fire, who in theory is supposedly very powerful. In practice, it seems, less so - she's only mentioned once, and even then there's speculation that she might have died and been replaced by her son (not her daughter, I note). I've always interpreted this as a relic of the more common model - that the te-Vikram began like other Vulcan societies and it's slowly given way to something else (something unusual in Vulcan terms), but it still retains this last symbolic remnant, the ghost of the idea that the male administrators, warlords, businessmen, etc., are loyal to or serve a more distant matriarch with a more detached, more encompassing, "spiritual" authority.
Or, to answer the actual question (

) I've assumed the relationship might be quite distant. But I'm sure
Uncertain Logic will give an answer.