The Answer:

Think about the noun you are using. Everything after the noun is modifying the noun, so what you want to do is simply make the noun a plural: mothers-in-law.

This goes for other compound nouns, too. The plural of heir apparent is heirs apparent; of attorney-general is attorneys-general; of man-of-war is men-of-war; of notary public is notaries public; and so on.

—The Editors