I can see the Communist Nations declaring the UN useless and leave and set up their own UN equivalent.
No the Communists have no reason to leave the UN. The situation as described by The Red based on the OP's scenario is that the North Korean invasion (in response to southern Korean incursions don't forget) is submitted to the UN Security Council and the resolution(s?) that were voted for and acted upon in OTL are vetoed by the Soviets in council. Then the USA and the British invade anyway. The Soviets can sit back and use the full majesty of the UN as it tears itself apart as a soap box to (rightly in this instance) condemn the USA and Britain as treaty breakers, war mongers and trying to set up one set of rules for themselves and another for the rest of the world.
If anyone leaves or indeed is expelled (I'm not sure about the mechanism for that) it would be the USA and the British.
The Soviets have as I say no reason to leave and every reason to stay whilst the Americans and British destroy the UN. THEN they can think about sponsoring a new organisation which would of course consist of far more than just the Communist world, it would be nearly everyone infact apart from the USA, Britain and a few other members of the anglo-sphere.
Which is why the whole idea of the USA and British sending significant troops to the south to oppose the northern incursions is more than a little unrealistic. What might happen is that we migh end up with a proxy war or the rest of the world lets the Koreans get on with it. In the former case it is anyones guess who wins (unless the Chinese get involved - they of course are not bound by the UN as they have been blocked from doing so by the USA), in the event the Koreans are left to sort it out the North Koreans win.
Japan is the Pacific Finland it has been demilitaried, the only difference is the USA demilitarised it instead of the Soviet Union.