Well, I have spoken to my elders who were uprooted from Punjab, and non-relatives who left Sindh more amicably, as children. Their view, despite being informed by personal experiences, was far from what you mention. When their families had lived there since time immemorial, obviously they felt hurt seeing what had earlier been brothers, seek to expel them violently from their ancestral lands. But I've never heard one of them holding an ill intention towards Pakistan as a state or its people. Most felt the happenings to be God's will and nothing more, so they accepted their fate, be it sleeping with empty stomachs on railway tracks or seeing their relatives murdered before their eyes.
Those generations moved on, as is evident through their actions upon your state's creation. I need not remind you who initiated all the wars as you can refer to Asghar Khan or any neutral source of the time. Even before Pakistan was created, Jinnah all the way up to '46 was pushing for the cabinet mission plan, whereas Nehru & co. repeatedly refused and preferred partition. So after seeing who wanted what, it is more likely that Jinnah hearts of heart did not want what happened rather than Congress not accepting Pakistan after giving its share of the treasury and refusing other options on the table.
But it helps many in Pakistan to sleep better at night thinking that India does not accept your existence, hence you are threatened and occupy the moral high ground in any pre-emptive measures to secure your "survival". Believe what you want, but I hope you realize how ridiculous it is for India to not accept its neighbour as a state when it is a reality and fact that came about as a result of our own decisions, good or bad. The sentiment here is unreservedly that we want to live peacefully and focus on our masses, not be irritated on occasion by invasive attempts to ensure your uncompromised "existence". Live and let live.
I don't think India wants to annex anybody, just that it prefers positive relations which rule out war or other distractions and allow us all to focus on the common person's misery for once. The majority of our people were left so economically deprived at partition, that they, neither then or now, cared about 'influence', 'politics' and other things which interest relatively well off people like you or me, but just want to get on with life uninterrupted and see their children happy.