This debate seems to rely on a couple of printed authorities (like the Cambridge Guide), but this construction is so low frequency that most grammars donʼt have any information on it. Few native speakers ever need to use it, so intuitions are hard to access.
The comments so far ignore the fact that syntax is not "flat"; grammatical units are grouped into hierarchical units. The plural of nouns belongs to the simple category of the noun, but the genitive/possessive belongs to the entire noun phrase, as proven by phrases like "the queen of England's crown" (not *the queen's of England crown): in
[[the queen of England]s crown], the possessive S belongs to the phrase "the queen of England".
So the plural of "brother-in-law" (at least in the standard language) is "brothers-in-law", since the plural goes on the bare noun. The possessive cannot be *brother's-in-law; it has to be "brother-in-law's", and that is what native speakers say ("We went to my brother-in-law's house").
By this logic, the plural possessive should be "brothers-in-law's" (no matter what any guide says!), but at least where I come from, the colloquial language resolves it as "brother-in-laws'". We tend not to non-standard plurals (e.g. two brother-in-laws, two attorney generals). Let the purists cringe, but it's a more natural, "English" solution.
The readers of this post should decide who they trust more--a pronouncement from a guide on a low-frequency construction, or the intuitions of millions of native speakers of English. What would most people produce and/or comprehend?