This thread is one part AH challenge and one part floating my solution to that challenge.
The Challenge: With a POD no sooner than 1790, have Manchuria and Korea ruled by the Qing dynasty as budding kingdom in personal union by 1865 or so.
I offer my solution in part to explain just what I mean and in part because I've been toying with the idea. Say a powerful anti-Manchu, anti-Qing dynasty revolt begins in the 1840s. There a number of possibilities (stronger, earlier Taiping; something organized by those protesting against an "Occidentalizing" emperor, perhaps with the help of Lin Zexu; a dynastic squabble). British aid to the Qing (ironic since it will probably have been something like an Opium War that prompts the rebellion) is effectively countered by another foreign power (probably a strong France, but aslo perhaps Russia). With strong bases in southern and central China and a provisional capital in Nanking, the rebel dynasty seizes Beijing in 1850 or so. The European powers force a peace treaty which recognizes a Qing kindom of Manchuria. The British pour money into the Qing as a bulwark against Russia. The Qing effectively assert their dominance over the Joseon dynasty in Korea, a traditional Chinese vasal. In the 1860s, no successor to the Joseon dynasty can be found. [IOTL, the Andong Kims found a "lost" member of the dynasty who seems to have largely been a puppet; something similar could happen TTL]. The designated successor to the Qing throne is married to the last female descendant of the Joseons [optional, since it wouldn't really be necessary nor assure transmission of dynastic rights, but it might allow for some kind of settlement to an internal power struggle].
Thoughts on the overall plausibility of such an event or on potential details to make this happen? I'm not sure Chinese dynastic theory or East Asian culture (either Chinese, Manchu, or Korean) would really allow such a development, but it has the potential for interesting three-way dynamic between a very strong Manchuria-Korea, Japan, and a southern-focused China.