Well Nehru's family was originally from Kashmir so I'm guessing that he probably still had a fair amount of family there which might possibly throw a spanner in the works. Plus IIRC whilst the princely state of Kashmir and Jammu was majority Muslim, Jammu was mostly Hindu and I think it was the eastern part around Ladakh actually had a large amount of Buddhists. A decent idea might be to partition the state with Jammu going to India, Kashmir to Pakistan, and Ladakh could go either way and have some interesting consequences.
An amicable split whilst still having the clusterfuck of partition is going to make relations between the two countries much more amicable, although I doubt they'd be bosom buddies. Come 1962 if the China decides to press their territorial grievances militarily then whoever got the east of the state is going to come into play - if India received it then it remains a wholly Sino-Indian affair as in our timelime, if Pakistan received it then you could be looking at a two simultaneous conflicts. Having a mutual enemy could see them working closer together. In our timeline India apparently liked to stir up trouble in Afghanistan as a way of inconveniencing Pakistan and giving them another problem to deal with whilst China backed Pakistan to help mess with India. With no real hostility India's monkeying around in Afghanistan doesn't happen and if the Sino-Indian War becomes the Sino-Pakistani/Indian War then Pakistan certainly wont be allying with China, who IIRC helped a great deal with their nuclear weapons programme. A western orientated Pakistan with a hostile communist China on their border is likely to see large amounts of American air roll in, at least until the mid to late-60s. The hostile border, and possibly occupied territory however would probably unfortunately mean that the military is still able to take a fairly large slice of government funds and associated national influence.