As of today, June 3rd, P. is officially an American citizen. I attempted to teach her the pledge of Allegiance but I've somehow forgotten the middle part.
There was a small problem because O.'s name is different on the 3 main documents- his passport, P.'s birth certificate (Indian) and our marriage certificate. It all worked out in the end when we wrote an affidavit stating that O. is know by all these 3 names and that the name on our marriage certificate is spelled wrong, but he prefers to go by ---.
In the end we'll get P.'s passport, and report of birth (birth certificate) in the mail in a couple weeks and her SS# in a couple months. All in all, much easier than giving birth in the US.