By the time China entered the war, the invasion was already over. China entered the war for two reasons: 1) to make sure China was not invaded as MacArthur intended 2) to keep North Korea alive as a buffer, not to help invade South Korea. There was nothing to gain for China if the North unified Korea. Their relationship wasn't that good in the first place.
By the time China entered the war, the invasion was already over.
I don't see any substance the point you're trying to make here. One could try to say, "China was only trying to preserve North Korea's borders prior to the invasion". But once it pushed further south, into South Korea proper -- it was joining the invasion. There's nothing to debate here.
1) to make sure China was not invaded as MacArthur intended
And this just makes no sense at all.
MacArthur never intended to invade China, and didn't even start making noises about bombing China until after the it joined the war effort.