I will be flying with my 5 year old daughter without the mother to Mexico from Germany with transit in the United States. Her grandmother on her mom's side will also be traveling with us.
I was born in Mexico and have acquired German citizenship and kept the Mexican one. I will be traveling with my German passport. I am separated from the mother (she is German; we were never married), but I still have a good relationship with her. My daughter was named according to Mexican law, so her last name is my first last name and her mother's (maiden) last name (to give an example with a fake name: Ana Maria González Müller). Something to note is that the mother has since married someone else and took his name, so her last name is no longer the one on my daughter's last name.
I bought the ticket through Lufthansa but I believe the airline will be United Airlines.
My question is: Is there something I should consider while traveling with my daughter regarding boarding the plane, going through customs or similar? Should I get a signed letter from the mother or something? I will be for sure carrying her birth certificate. What else can I do or take with me?
Edit: -The mother and I have shared custody. -To clarify, I will be entering Mexico with with my Mexican passport as it is required by Mexican law. My daughter has never been to the Mexican consulate in Germany and hence has no Mexican passport or birth certificate.
Update: We will be writing a letter of consent in English, German and Spanish, and we will go to the city hall to get the mom's signature notarized
Follow-up: We are back in Germany and everything went smoothly. I took with me a bunch of documents from my daughter including vaccination certificates, but all that was needed was the notarized letter of consent from the mother at the passport control when leaving Germany (apart from the passports and ESTA, of course). For future reference, we got the signatures on the letters notarized at the city hall (Rathaus) and it costed 1,50€ per stamp. Thanks to everyone who answered and commented!