Depends.

It depends on whether she was granted full/sole physical and legal custody of her kid.
See the following at:
https://www.us-passport-service-guide.com/can-one-parent-apply-for-a-childs-passport-without-the-consent-of-the-other-parent.html


Question: I just recently finished family court and was granted full/sole physical and legal custody of my daughter. The father name is on the birth certificate. Do I still need his consent or can I fill out a DS-11 form and attach the court order with it.

Answer: Since you were awarded sole legal custody of the child, you no longer needs the father's consent. You may proceed with applying for your child's passport and submit the court order with the application.



Related information also can be found at:
https://www.us-passport-service-guide.com/child-passport.html