I don't know what Shenyang you are referring to. The only Shenyang I know is a city in Manchuria region.
The relation between China, Korea and Dai Viet during the EU period was more like a mini HRE, with China as the permanent emperor and Korea and Dai Viet as Kingdoms. China serves as the leader in name, and protects the kingdoms (Ming and Qing both tried to protect Korea from Japanese invasion. Ming's occupation of Dai Viet around the 1400s was also because of the "request of the old dynasty" to "remove the rebel dynasty". There was no PU ever existed.
The only real PUs in Chinese history of EU period were the relationship between Qing and Tibet/Mongolia. Qing Emperor is also the Khan of outer mongolian region (this happened during the Tang Dynasty too), and one of the religious leader of Tibet (Qing Emperors were considered as the avatar of "Manjusri", while Dalai Lamas were considered as the avatar of "Avalokiteśvara"). Also because of this reason, Qing emperors had royal marriages with Mongolia. For example, Empress Dowager Xiaozhuang was from Borjigit clan, and was a descendant of Hasar, a younger brother of Genghis Khan. However Qing's PUs are relatively more centralized compared to European PUs.
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