I was just reminded of something I was supposed to connect before but never did.
So, I think it's pretty well-established at this point that Eirin is supposed to be Omoikane. In CiLR 1, Eirin explains that the Watatsuki sisters are distant relatives of hers; "one was the wife of a grandnephew of mine, while the other was married to the son of another grandnephew". I had always meant to explicitly connect the dots here.
First of all, I'm going to change this translation since it isn't "another" grandnephew, it's the same guy. With the clean assumption that Toyohime and Yorihime are supposed to be Toyotamahime and Tamayorihime respectively, it's actually that this "grandnephew" is Hoori. Hoori married Toyotamahime, and they had a child (Ugayafukiaezu) who later married Tamayorihime, which fits the above narrative.
Hoori is the son of Ninigi and Konohanasakuyahime (who you may also know as the one who cut Yatsugatake). Konohanasakuyahime is herself descended from Ooyamatsumi, who apparently came from Izanagi before his cleansing (which spawned Amaterasu, Tsukuyomi, and Susanoo, among many others). Ninigi on the other hand came from Amenooshihomimi and Yorozuhatahime. Amenooshihomimi came from Amaterasu, which as said above came from Izanagi. Yorozuhatahime came from Takamimusuhi, who is one of the three kami of creation. It's extra confusing since Takamimusuhi did some stuff, then left existence and reappeared generations later to have Yorozuhatahime -- but before they "hid", they created Omoikane. So to follow all this back down, Omoikane is a sibling of Yorozuhatahime, whose child is Ninigi, whose child is Hoori, who married Toyotamahime.
So essentially what Eirin did with this quote is further confirm her identity (along with the Watatsukis), but also troll a whole lot because the Shinto kami genealogy is convoluted as fuck and there were a ton of other ways she could have stated their relationship.