You should obtain a child travel consent letter granting you permission from the absent parent to leave the country with your child (having it notarized is not required, but highly recommended).
A letter of consent, preferably in English and notarized, from the other parent or signed by both custodial parents. The letter should say: "I acknowledge that my child is traveling outside the country with the name of the adult with my permission."
Is a minor travel consent form required for domestic travel? No, a minor travel consent form is not required for domestic travel within the U.S. However, it is recommended that parents and/or legal guardians carry a notarized letter of consent when traveling with a child.
There is no documentation requirement for domestic travel in the US for children flying with a parent. I've flown dozens of times with no one saying boo.
It's important that you give your co-parent notice and preferably get their express permission in writing if you wish to travel outside the state with your child. If the other parent refuses to cooperate, you can ask for the court's permission in advance.
Typically, minors under the age of 18 do not have to present identification for domestic U.S. travel. Airlines will accept identification from the responsible adult on behalf of the minor(s). For international travel, minors under the age of 18 must present the same travel documents as the adult.
The letter should include the other person's contact details and details about the trip. It also helps if you've: evidence of your relationship with the child, for example a birth or adoption certificate. a divorce or marriage certificate, if you are a single parent but your family name is different from the child's.
In the USA, though, unless there's a court order requiring permission from both parents, a child may travel (even to overseas) with either parent/guardian without showing proof of permission from the other parent.