If you are visiting another country — including Mexico — by yourself with a child under 18, you need more than just the usual travel documents. To help prevent cases of parental abduction, many countries now require proof of your relationship to the child and your legal right to have them accompany you in and out of the country.
This is not just an issue for single parents, but also for grandparents, adoptive or step parents, guardians, and even two-parent families traveling together — if a travel glitch makes it necessary for family members to travel separately, the additional documents will be necessary.

What do you need?  One or more of the following may be applicable: 
- A letter of permission from the absent parent(s) signed before a notary public and including details of the trip, the child and the accompanying adult, should always be carried. Have a copy translated into the local language, if possible. For further information see the blog post Sample Permission Letter for Traveling Child
ALTERNATELY:
- A legal decree of divorce showing that you have sole custody.
- A birth or adoption certificate which lists you as the only parent.
- A death certificate if the child's other parent is deceased. 

For more information visit the U.S. Dept of State travel site or talk to your AAA travel professional about additional requirements in the countries you are visiting.