That's accurate no issue here. Mughal empire fine, but the other two were enemies of ours and hence a separate identity emerged from that. So I will add some details.
We can go back further and if you look it wasn't part of the Punjab region, in the Ancient Period (before c. 1000 CE)Most of present-day Azad Kashmir (especially Muzaffarabad, Neelum Valley, Poonch) was culturally and politically linked to the broader Kashmir region, centred on the Kashmir Valley. It was ruled at various times by kingdoms such as the Karkota Dynasty and Lohara Dynasty. It was generally not administered as part of the Punjab plains. During the Medieval Period (1000–1586) local hill chieftains ruled many areas, Poonch and surrounding districts were often connected to Kashmir rulers, though control varied. The region remained part of the Himalayan hill zone rather than the core Punjab region.
Now going back to the Sikh empire, our people won a magnificent victory in 1810, in the battle that was fought in and around the Poonch–Rajouri/Bhimber area. The Sikh empire was only defeated two other times in battle in present day Pakistan that was the Battle of Attock (1813) and the Nowshera Campaign (1823), both fought by the Pashtuns. Sure their empire won through but that further developed our identity as fierce independent people. The Dogra scum were gifted their part by the British and were hard to defeat due to the British being their benefactors. With the the Second World War around 90,000 of our men enlisted, despite the cries of the Dogras. When the partition happened, we wiped them out as the British couldn't care less. This was primarily fought by us, Pashtun help came later and then the regular Pakistani army.
We do have a unique identity, but that doesn't change the fact that we are Pakistanis and fought to be part of the union. Only the Northern Areas also did that . We should settle things amicably between us.