Divorced mothers want to take their children to travel abroad. What should they do without father's power of attorney?

Correct a common sense mistake. Both parents, whether married or divorced, are legal guardians of their children before they reach adulthood.

The father of the child still has custody, and if anything happens to the child, he will be responsible.

The divorced child has been with you all the time, just saying that you raised the child. You only have custody, not custody. Legal guardianship is the most important right and obligation of parents to their children. Your ex-husband refused to entrust notarization, so you can only try to persuade him, or simply take his office card to entrust it to Guangdong, otherwise the child can go abroad when he is an adult.