In the west Pacific, China mostly relies on their navy and air force, while they will rely on their ground troops on the Indian border. By the time they will need their ground troops on their east coast, they will be in a lot of trouble, as in a full scale foreign invasion is happening and their navy and AF have been wiped out...
I don't think there will be a war between China and India at this time, based on the reactions of both governments. They are mostly quiet despite the emotions on the Indian streets. The Indian military might want a fight to avenge their defeat in 1962, but they don't make decisions. I am coming to believe that the Chinese had won the hand-to-hand combat so lopsided that the Indian military is thinking twice about fighting now. Also, the Indians had been bolstered by their preparation in the regions for the past few decades. They thought they had the superiority. Yet, for the past few weeks, the Chinese just demonstrated their capability to mobilize so quickly and efficiently to the potentially troubling sites. I think this whole thing will go away quickly.
