My kids have two US citizen parents. My ex refused to sign anything. I had to wait until each was 18 to get their own passport. No exceptions granted. I am in NJ. Not saying there are absolutes but I was given no options. couldn’t take my kids on vacation out of the country.
Couldn’t even buy a result. Very rare for NJ.
You should have gone to NY. I have been traveling alone on my own passport since I was 10. My father never signed anything.