Kaiya

Hello everyone, A brief on my own situation: I am from Vietnam. I have 2 illegitimate children ( aged 5 & 6) with my ex American boyfriend. He lives and works in USA. We stopped contact 3 years ago and he also stopped contributing for the kids since then. In their birth certificate, I am the only parent and according to law in VN, I have the sole custody of the kids, although there is no such document is granted, the birth certificate say it all. It is not available to provide court order or sole custody document in my case. To US law, the kids have both parents (they have report the birth abroad at US consulate and they have US passport. I don't have their original passport, the father kept them) My question is I have sole custody, do I still need the biological father to write a statutory declaration? If I do, then why do I need permission of somebody who lives in USA and is USC (not Vietnam) to remove the children from Vietnam to Australia? What if I provide form 1229 signed by me which states basically the same thing, plus my written statement of former relationship which will explain more (I have evidence to prove I was physical abused by him and he was no good to his own children...etc), should that be enough? Anyone here has gone through process and have the same situation, please share your experience. Any advice and info will be appreciated.