Jackie harrumphs®: I still say it should be parents-in-laws'. Bingley, since you are unsure... the only person whose uncited word I will take is Nicholas'.

And since Nicholas's [sic] word isn't here, I'll leap into the breach: "in-law" is a descriptive, and in English we don't pluralize adjectives. So I go with "parents'-in-law." For analogies, look at "attorneys-general" and "passers-by."
Having said that, I agree the construction is awkward and should be proscribed post-haste.