Yes, it would definitely be too late for your friend to write a recommendation for your daughter now.
By the way, even if your daughter were not to initiate into the sorority she has joined, she would not be eligible to receive a bid from Pi Phi for a year. This is an NPC regulation - no woman that receives a bid from one sorority during formal recruitment can receive/accept another from a different sorority for a one year period.
As far as little sisters for fraternities, they are now forbidden by most if not all of the NIC organizations. On some campuses, they still operate contrary to national policies. Many fraternity little sister groups that acted as de facto sororities actually became NPC sororities in the 1980s when the groups were made illegal.
Personally, I would not encourage a young woman to join these groups as I have heard many negative things about the groups still in operation. But I can't speak for every group and every campus.
Your daughter seems to be great and dealing with recruitment disappointment in the normal, natural way. I really hope she is growing to love whatever sorority she joined. Maybe you could use GC as an opportunity to learn more about the history and rich traditions of that group.
I know my mother, who went to a women's college that did not have Greek life, was rather opposed to me joining my sorority, but grew to love Pi Phi in the four years I attended college. She will tell anyone who asks that Pi Phi is the best! I hope that you will come to feel the same way about your daughter's new sorority.
My advice to you right now is honestly to let go. Everything usually works out as it is supposed to!