Part of me wants to sound like my mother and go, "Well, you should have thought of all that before...." blah blah blah. But what's done is done, and the past can't be changed. So I'm not going there.
The other part (the majority of me) deeply sympathizes with you. The system is right for punishing dads that don't do their job, but that makes them unfairly harsh to fathers that get caught up in a bad situation. My ex went through similar things with his daughter's mother.
She crossed a line when she told Jacob you weren't his father. Really. For more reasons than I can count, he has a right to know who his father is. And she had no right to move away like that.
"The entire world is being driven insane by this single phrase: "My religion alone is true." ...Who can make a system from Divine Mystery? But if any sincere practitioner, within whatever culture or religion, prays and meditates with great devotion & committment to Truth alone, Your Grace will flood his mind and heart..." ~~Ramakrishna
"Ignorance: The Verbal Airborne Disease" (c) my friend Ty