Fear of nuclear proliferation cannot be the reason China allows India with 1.4 billion hostiles to exist. India's superpower delusions ensure they will continue to be a huge threat to China. Its too big and if it gets good at anything, it will be a huge threat.The main problem with a broken up India is that instead of one nuclear-armed power, we end up with many nuclear-armed powers. India by itself is pretty predictable, and despite its numerous border clashes and short wars, we can be confident that these nuclear weapons will never be used. With multiple smaller nations, this is much less certain and the chance of nuclear conflict becomes much higher.
Nuclear risks can be managed by heavy international pressure to supply all the nukes to only one state. This is how it was done with soviet union breakup. It can be done again.