Origin and history of cotquean

late 14c., "a cot, a humble habitation," as of a farm-laborer, from Old French cote "hut, cottage" + Anglo-French suffix -age (according to OED the whole probably denotes "the entire property attached to a cote"). Old French cot is probably from Old Norse kot "hut," cognate of Old English cot, cote "cottage, hut," from Proto-Germanic *kutan (source also of Middle Dutch cot, Dutch kot).

Meaning "small country residence or detached suburban house" (without suggestion of poverty or tenancy) is from 1765. Modern French cottage is a 19c. reborrowing from English. Cottage industry, one that can be done at home, is attested from 1854. Cottage cheese, the U.S. name for a kind of soft, white cheese, is attested from 1831, earliest in reference to Philadelphia:

There was a plate of rye-bread, and a plate of wheat, and a basket of crackers; another plate with half a dozen paltry cakes that looked as if they had been bought under the old Court House; some morsels of dried beef on two little tea-cup plates: and a small glass dish of that preparation of curds, which in vulgar language is called smear-case, but whose nom de guerre is cottage-cheese, at least that was the appellation given it by our hostess. ["Miss Leslie," "Country Lodgings," Godey's Lady's Book, July 1831]

Middle English quene "a woman; a low-born woman," from Old English cwene "woman," also "female serf, hussy, prostitute" (as in portcwene "public woman"), from Proto-Germanic *kwenon (source also of Old Saxon quan, Old High German quena, Old Norse kona, Gothic qino "wife, woman," Middle Dutch quene "vain or worthless woman"), from PIE root *gwen- "woman." Compare queen (n.). The -ea- spelling is attested from early 15c.

Woman considered without regard to qualities or position (perhaps by contrast to the senses in queen), hence often a slighting or abusive term for a woman; in Middle English it could mean "a harlot; an old woman or crone," and it was in popular use 16c.-17c. in the sense of "hussy." But in Scottish often with a sense of "young, robust woman" (late 15c.).

The sense of "effeminate homosexual" is recorded by 1935, according to Partridge this was especially in Australian slang.

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.