PC: Toyotomi Korea and Tokugawa Japan

Say Toyotomi Hideyoshi is successfully in conquering Korea. Could his Son still lost control of Japan to the Tokugawa Clan while retaining Korea ?
 
The two biggest non-self-inflicted challenges the Japanese had to deal with during the Imjin War were 1. the Korean navy and 2. insurgencies in occupied territories. Buddhist monks in mountain monasteries and yangban-led peasant 'Righteous Armies' constantly harassed Japan's already overstretched supply lines independently of the Joseon and Ming armies. Seeing how poorly received the Japanese were during the war by the populace, it's doubtful that a Japan in the throes of civil war between the Toyotomi and Tokugawa will be able to maintain control over Korea, especially considering the war would be within a generation of the Imjin War (if we're going with Hideyori losing control of Japan).

There's also the Jurchen/Manchu to account for, with Nurhaci having offered to help the Joseon expel the Japanese during the Imjin War and the Japanese attacking Jurchen territories during the war. The Manchu rolled over the Korean army OTL twice without any help and that's without the Koreans having to deal with insurgencies elsewhere. Plus, reinstating the Joseon dynasty would be easy, with how unstable the Japanese regime would be, and would score Nurhaci brownie points with the Joseon and the Ming, which he was going for when he offered to fight the Japanese during the war. It'd give him a valid excuse for grabbing supplies from Korea that would help with future wars with China, prevent the Chinese from being too hostile with him early on while he's still consolidating, and secures a neutral or allied southern border (which Hongtaiji would do later on after the more neutral/pro-Manchu King Gwanghaegun was overthrown in favour of the pro-Ming King Injo) that owes him a favour, rather than a regime that had attacked his lands without much reason very recently and would serve as a liability (since Joseon loyalists would side with the Ming if the Manchu don't support them instead, and that means committing troops to subduing Korea while fighting with the Ming and potentially Tokugawa, which isn't exactly a sustainable model long term).

Most of the Toyotomi power base would be lost if the Tokugawa take over the home isles, which leaves the Toyotomi and their allies in a precarious situation if they retreat to Korea, where they likely won't have much support amongst the locals and not enough time to build any sense of legitimacy or loyalty, seeing as they were invaders that brutalised the peninsula just a few decades (or less) ago.

This is compounded with the fact that the Tokugawa will not suffer the Toyotomi exist any longer, as the Toyotomi are a direct threat to their legitimacy as the hegemon of the Japanese islands (the tozama daimyo of OTL who sided with the Toyotomi were sidelined for over 200 years after the fact and ended up overthrowing the shogunate, after all). A resurgent Toyotomi clan would naturally try to reclaim their ancestral holdings and powerbase, especially with how much of the archipelago sided with them when push came to shove and still remained loyal/bitter against the Tokugawa, which is a threat the Tokugawa would have no reason to not try to kill in the cradle before it can actually manifest.

So the Toyotomi will lose all the lands they actually had effective control over, they'd be stuck with rebellious holdings that are liable to uprisings and invasions from the north, and the Tokugawa will try to end the Toyotomi at the first opportunity to remove the security risk.

I'd say it's not very plausible, unfortunately.
 
Say Toyotomi Hideyoshi is successfully in conquering Korea. Could his Son still lost control of Japan to the Tokugawa Clan while retaining Korea ?

Color me skeptical, assuming Hideyoshi "wins" in Korea in the first place, does he still have his nephew and closest living male relative Hidetsugu killed? You would also have to ask yourself how does Hideyoshi win in Korea but lose in China? What happens to Korea does it's eight provinces get given out to Korean Shugo, and do we see the phenomenon of Korean daiymo.

Also, Does Hideyoshi still die as in OTL? If Hideyori is even a chance of a successful regency, then I doubt Ieyasu can make a play for power, this is even assuming Sekigahara goes the same way.
 
Yes

Not sure maybe no admiral yi
Admiral Yi was very successful during the Imjin War but 1. he wasn't the only major naval figure during the war and 2. the destruction of most of the Joseon fleet and his most major victories were won in the 2nd phase* of the war, after the Japanese had been successfully pushed back after their initial offensive, the Ming had intervened, and a ceasefire held for a few years during which unsuccessful peace negotiations were held (and fell through). During the 2nd phase of the war, the Japanese were unable to make half the gains they made during the 1st half, despite still managing to land entire armies without impediment (most of the Joseon fleet being destroyed in the opening stages of the 2nd phase) in both phases of the war.

*The Imjin War involved 2 separate Japanese invasions, as there was a ceasefire after the Japanese were pushed back from Pyongyang all the way to Hanseong during the 1st phase and a stalemate was reached at the middle of the peninsula.
Yi's legendary 13 v 133 victory at the Battle of Myeongnyang was in the 2nd phase, when Japan's victory was all but assured.

While Admiral Yi performed admirably, the survival of the Joseon kingdom didn't seem to hinge on him alone, but rather the combined efforts of the guerilla forces throughout the peninsula, the naval forces (of which Yi was one of the most prominent figures, true), and the overextended of and bickering between Japanese leaders as they became drunk on success due to their rapid advance (which was followed by almost just as rapid a retreat as soon as an organised force opposed them).
 
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