Children traveling with only one parent
I've bought a ticket and the website has a reminder that since I'm traveling with my children by myself (not with my wife), that they recommend I take my child's birth certificate with me. Then I did some googling and found that US now requires the non-traveling parent to provide a notarized signed agreement that I'm traveling with my child. A paragraph from US GOVT website says I just need a paper that says "I agree with my spouse taking my travel for travel" and sign, no notary needed.
Anybody with experience with this, traveling with your children without your spouse, do they really ask? If yes what documents did you bring with you? (Notarized, just signed, birth certificate, etc.)
Thanks in advance.