You can, and mostly do, want to hold Seoul. Here is how to do this:
Send your Busan division to Seoul in combat ready (default) mode, the Korean troops will follow.
Land your landing boats on either side of the peninsula before retreating back to avoid coastal guns.
Set your Japanese air base to fighter patrol but do not touch your strategic bombers just yet.
Get your three Japanese divisions in your army base and fly them over to Seoul.
Set your production to 80% or more and queue up divisions, spawn them in Japan and fly them over to Seoul when they are available.
Whenever troops reach what is the DMZ nowadays, order them to entrench.
Set your research to better small arms (or whatever the AK research is (the first one in the infantry tree)).
Keep doing this (switching to 100% production if needed) and you will hold Seoul.
Do not cross the border into North Korea yet.

If your divisions are not holding the DMZ and entrenching yet DO IT NOW, the Chinese are coming and they pack some seriously nasty stuff.
This is also about the time the DRPK will start sending aircrafts your way so do this:
Divisions galore to HOLD THE DAMN LINE, if you haven't seen the Chinese army yet, keep building.
Build a tactical airbase in the middle of your share of Korea to assert air superiority, set the fighters to patrol.
Your fleets should be near Japan by now, send the bigger one in between China and the DPRK and the smaller one next to the North Korean city that hugs the russian border, set them to patrol with their fighters.
Queue up the basic anti chemical warfare suits technology for your army division, the soviets love mustard gas and that thing is SCARY, better be prepared for your war with them (you are going to war with them don't worry) (this is a tier two infantry technology that will also queue up better infantry equipment) and then queue up IFVs (Infantry fighting vehicles (tier 2 infantry technology).
By now you should be fine on the land side of things, feel free to push into Pyongyang and demolish DPRK military infrastructure but DO NOT PUSH INTO CHINA (though your fleets can hug their coast and shoot at their stuff).
If you are comfortable with it, I recommend increasing research spending, if not you may be attacked by the Soviets before getting mustard gas resistance and will have to sue for a ceasefire to buy time.

By now you should have a high tech land force and terrorise the Chinese coast but the fight is not over yet. Now you must:
Annex North Korea (easy enough)
This will trigger a war with the soviets if that wasn't done already, just hold the border for now (but do feel free to cross into China).
I heavily recommend building a tactical airbase in N.K. to prevent airborne bullying.
Now you are going to want to assert naval dominance, by now the soviets will start being vaguely threatening with their fleet and the Chinese will throw a couple of destroyers your way. Anyway, send destroyers to the Russians and cruisers to the Chinese.
Feel free to use spec ops to demolish enemy air defense.
And now just hold, I recommend switching to 100% research and researching as many plane-related technologies as possible (these will come in handy in the next scenario: the Cuban missile crisis (yes, technologies are transmitted from mission to mission))