You have a fundamental misunderstanding here. We have not " picked" India because of Pakistan. We've picked India because of India. We are the ones who are helping you kill the terrorists and paying you. They are not. You are important to us but not that important to this decision. A decision which has been play for almost 10 years now.
China is beyond an ally for you. Pakistan has been trying for the longest to have China's have many military bases in Pakistan. You don't sell off a port because you are just an ally. You don't give another full access to your sovereign land because you are just an ally. That is precisely what you've done Gwadar and in the North too.
They built that port, charged you a heavy interest on that loan, made sure 90% of workers were imported from China and 100% of no bids contracts went to Chinese only companies. And then they have taken over it.
Now to my knowledge( which 6 months or more before I retired), they had yet to move their naval assets to the port and on a permanent basis. But it is only matter of time before that happens. Problem is that Chinese are of two minds on this, they are worried about the optics and security .