I have made a crusade out of correcting misplaced plurals like “mother-in-laws” to “mothers-in-law.”
But why doesn’t the possessive follow the same rule? Why is “mother-in-law’s” OK?
Because possessives and plurals are two different things, and thus don’t have to follow the same rules. You might as well ask why don’t nouns and verbs follow the same rules.
As for the reason for it – I’m guessing euphony has a lot to do with it.
Because the plural s attaches to nouns, and the possessive 's attaches to noun phrases in English. The plural s is a remnant of noun inflection, which the 's is effectively a particle linking two words or phrases.
Why shouldn’t it be? The plural morpheme /z/ normally attaches to a noun, even if it’s part of a larger noun phrase. So with phrases like “King of Siam”, if you want the plural, it’s “Kings of Siam.” Whereas the possessive clitic (also usually pronounced /z/ but spelled with an apostrophe) attaches to the end of a noun phrase. So you have “the King of Siam’s big dance number” or “my mother-in-law’s big fat mouth”. “Mother-in-law” works basically the same as “King of Siam” or “girl from Ipanema” or any other similar phrase.
The same is basically true of all such nouns, including other nouns that were the result of direct calques from French: attorney general, court martial, and so on. Basically, we treat them as noun phrases - the plural ending attaches to the head noun, but the possessive ending attaches to the end of the phrase. That’s just how it works in English.
Of course, these noun phrases have a tendency to be reanalyzed as single nouns - some people who haven’t been taught otherwise pluralize “mother-in-law” as “mother-in-laws”, and even moreso with less transparent phrases - “courts martial” is used in formal writing, but “court martials” is by far the more natural plural. They even get transformed whole into verbs - “court-martialed” is perfectly acceptable; there’s no alternative for foreign speech (martially courted, maybe? :)).
More examples:
My son and dauighter are both untidy.
My son and daughter’s rooms are both untidy.
My sons and daughters are all untidy.
My sons and daughters’ rooms are all untidy.
We disagree.
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My son’s and daughter’s rooms are both untidy.
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My sons’ and daughters’ rooms are all untidy.
Parse this perfectly well-formed sentence:
The son of the Pharaoh’s daughter is the daughter of the Pharaoh’s son.
There are four parsings, two of which are contradictory and two of which are tautologies.
How do you know that for sentence #2, giles didn’t mean that not only are giles’ daughter’s rooms untidy but that giles’ sons–not their rooms–are also untidy?
That’s just a slightly flippant remark. It points out the linguistic ambiguity of the expression in question. In this case, the writing of it tends to allay that ambiguity.