CHILD CUSTODY

Im a single mom. I have two with two different fathers. My first born is already 14years old. My youngest is 2years old. The father of my first born and i are not married and we separated because of VAWC. For the last years, my first born was under my custody. Only until recently that i have decided to let go of her and let her stay with her fathers family. The father is currently in Korea with no proper documentation. If in case the family of the father would process needed documents to bring my daughter to Korea, would it still need an approval coming from me? Or they can simply bring my daughter to Korea even without my knowledge? The father though had signed her birth certificate as acknowledgement.