Legal Question in Family Law in Arizona

It appears that yes, Canada will request a written document granting you permission.

Here is what I found:

Have the necessary ID for your children ready to present to customs officer.

Divorced parents who share custody of their children should carry copies of the legal custody documents.

The Canada Border Services Agency suggests identification such as an original birth certificate, baptismal certificate, passport, or immigration document. If none of these are available, get a letter stating that you are the children's parent or guardian from your doctor or lawyer, or from the hospital where the children were born.

Adults who are not parents or guardians should have written permission from the parents or guardians to supervise the children, including the name and contact information of the parent / guardian

Even if you are not divorced from the child's other parent, bring the other parent's written permission to take the child over the border. Include contact information so border guard can call the other parent if necessary.

Adults / Guardians should travel in the same vehicle as their children when arriving at the border.

Children old enough to speak for themselves may be encouraged to do so by the customs officer, so be prepared to let older children answer the officer's questions.