Just FYI ~~my sister ran into this problem with our upcoming cruise. If you are getting a US Passport for the boy, his non custodial parent will have to sign the application (notarized) if he is under 16. And you STILL should have altter authorizing you to take him out of the country. You never know what someone will do if they get angry enough.. and it is better to be safe than sorry.
Regarding her not wanting to sign something~ some people just aren't happy seeing other people happy!