You may have to keep Pakshi as first bird, meaning that you do things for her first so she knows her place since she was there first, that should help but with time I am sure she will realize she has to share your time with Rishi.
Then it was meant for you to have Rishi, he knew he liked you from the moment he met you and that is so sweet but that is how a lot of greys have made it into our lives, they choose us and not vice versa, thanks for sharing that story with us.
I will check out your profile for the pics, thanks.