SOLVED - PNR Prince of desert tribe (scorpion clan?) repudiates his wife

A favorite of mine

The Spider Prince by Rebecca Goings

This is a different book from The Spider Prince (Desert Princes of Jikkar Book 4), but the OP’s question reminded me of Courtship Rite by Donald Kingsbury

I’ve had to link to the Audible version, since the book is not available as an eBook, and is also out of print, although it was nominated for the Hugo award in 1983. Strictly speaking, this is science fiction in a future world which is fairly inhospitable to humans and also with no animal sources of life and limited protein options, but which was settled thousands of years ago. Three clone brothers are seeking to court their third wife, when they are ordered instead to re-direct their attentions outside their clan to Oelita, a biologist in a neighboring province, based on her “kalothi” — a personal quality which indicates fitness of survival, either because of personal skills, force of personality/ability to lead or convince others, or to make accurate predictions of how to optimize survival (for your clan, as well as yourself) in different circumstances.

At least one of the brothers decides to test the kalothi of this unknown woman by testing her ability to survive his courtship! The world building is great, and so are the personalities of all the characters — both the husbands and the wives, who are all very different. A lot goes into how they make their marriage work, and also the very devious, competitive society. Somewhat scandalously, they end up falling in love with both women, and having a family of four wives with the three husbands. And the interactions with each husband and wife is quite distinct.

The original story was serialized in Analog (magazine), and I later came across a copy of the book in a used bookstore. It’s one of the books that I wish would get published as an eBook.