No you do not have the whole picture. There were many princely states. India forcefully invaded them all despite promising not to or to allow a democratic vote. Hydrabad stands as muslim territory invaded by india.
The king of Kashmir is irrelevant... the power that be was Sheikh Abdullah who went against muslim aspiration but wanting kashmiri independence and massively damaged the muslim cause during partition.
You need to read beyond indian propaganda. Pakistan did not initiate anything. At the point of partition all the armed forces the british left was left to the indians. When trouble started british officers who were supposedly part of pakistani military refused to do their job and check indian aggression. Pakistan managed to save a lot of kashmir....hence azad kashmir...free kashmir.
Kashmir is muslim , hence not indian....same as hydrabad which is illigally held territory by india.
I also explained why it is a trilateral issue. What did you fail to understand? East and west pakistan separated for political reason. The need for muslim sovereignty remains, otherwise we would have joined india. The right of kashmiri muslim are as much our issue as it is of pakistans. The only difference is we are geographically not close.
Our ancestors fought for the muslim cause and our duty remains to carry on that legacy. Look beyond 1971.... our history is much older than that. We can have issues with pakistan on many issues .....but never when it comes to muslim sovereignty in the subcontinent. East pakistan renamed Bangladesh is an equal beholder of the two nation theory and Kashmir is a trilateral issue between India and the muslim states of Pakistan and Bangladesh.
Whose pecking order? Why do you care?