Ancient Latin had very precise terms for relationships between family members. Many languages do (although I don’t think any are as specific as the imagined one in Heinlein’s Citizen of the Galaxy). My Latin dictionary has an interesting page showing these terms in a family tree, but I don’t have it here, and haven’t been able to find anything similar in a quick internet search. I’ll bet they had a term ffor what the OP is looking for.
Contemporary English is sadly deficient in such terms. We end up labeling a lot of folks “cousins” of various sorts, or “great aunts/uncles”.
What I want is a term for what my sons’ in-laws (especially M&FIL) are to me (other than competition). Because I think that’s a relationship unlike others.
I’ve been tempted to use Shecky’s out-laws, and not because of any animosity.