Yes countries failed to stop Pakistan from gaining Nuclear arms, they also failed to stop North Korea, so it wasn't because of either country's military might but because they can't trust how your establishment would react in case a failed attempt was made.
So yes they wont take that chance but it all changes in case a war breaks out between India-Pakistan.
As far as India is concerned it has no first-use policy and a reputation around the world as a responsible nuclear power, Pakistan doesn't. So in that case, you become a worry for the entire world, including China. As a nuclear war in the region will hit everyone hard. You can figure out what would happen if that is the case.
About J & K, it's an internal problem of India. Something we have to deal with in a better manner definitely.
And are you seriously asking me why Pakistan has an image of irresponsible nation? it has been well established what years of unconditional foreign aid sent for war on terror was used by Pakistan for. And OBL episode just exposed how uncommitted you were to the war against terror.