Geez – this gets complicated real fast: Essential ID Requirements For Flying with Minors (msn.com)
If one parent is traveling with one or more children, the parent may need to have documentation to prove they are the parent.
If the children have different racial characteristics to the parent (which subjective), they may be required to have documentation and birth certificates (this is an issue in my own extended family).
Documentation may also included notarized, signed letters and documents.
It’s complicated – read the above link.