1540s (now obsolete), originally apparently "housewife of a cot," from cot "hut, peasant's hut" (see cottage) + quean "woman." "Thence the transition is easy on the one side to 'one who has the manners of a labourer's wife, rude, ill-mannered woman, vulgar bedlam, scold ...' and on the other to 'a man who acts the housewife.' " These senses -- "rude, ill-mannered woman" and "man who busies himself with affairs which properly belong to women" -- both are attested from 1590s. Related: Cotqueanity.
The Cucking-stool was a means adopted for the punishment of scolds and incorrigible women by ducking them in the water, after having secured them in a chair or stool, fixed at the end of a long pole, serving as a lever by which they were immersed in some muddy or stinking pond. [Willis's Current Notes, February 1851]
early 13c., from verbal noun from cuck "to void excrement," from Old Norse kuka "feces," from PIE root *kakka- "to defecate." So called because they sometimes resembled the old close stool of the pre-plumbing days, a portable indoor toilet that looked like a chair with a box under the seat. Old folk etymology made the first element a corruption of cotquean. For second element, see stool. Also known as trebucket and castigatory, it was used on fraudulent tradesmen, in addition to disorderly women, either for public exposure to ridicule or for ducking.