it would seem the rationale for
Our nukes cannot be used to deter any interference. They are used to deter Chinese nukes against us as are Chinese nukes to deter any nuke attack on themselves.There is the china factor in all this India clearly has to use the nuclear first strike threat against china for any interference and since we have already suffered a nuclear strike, it will not be prudent for china to interfere as it will have more to lose than India.
If the Chinese respond in conventional manner then we will have to do the same. What will be the objective of such an interference. If its not directed at taking over New Delhi or occupying large tracts of land, then our nuclear bluff 'for any interference' will not work with the Chinese.
However there is still a quandary to solve in your scenario of all out war accompanied with a Pak first strike..
In this scenario, pakistan has lost already lost the war and our troops are already in control of a lot of Pakistani territory. We cannot nuke our own forces.Its clear here that the Pak deterrent failed to prevent an all out war. Our deterrent will not stop a Pak nuke because they have nothing to lose at this point. So we would have to be out of our frickin' minds to take a lot of Pakistani territory.cities like Karachi, Hyderabad, Quetta cannot be nuked as it has people ready to break away from Pakistan and Indian forces will eventually be there.
An alternative scenario is Pak launches and we march in as a result because 'We have already suffered population losses due to **** strike.' This means our deterrent failed to protect us from a Pak nuke.
If both our deterrents are deemed to be effective there should be no chance of an all out war to begin with. Its out of the question and is what i would consider the major flaw in the scenario. The most we can expect is a short conventional border war or limited surgical strikes and nothing more. Another flaw is that it assumes that Pak + India's nukes can be used as an offensive weapon. Not the case.
To put it another way, for your scenario to work requires the successive failures of the deterrents of three countries in tandem.