Hi there. The Family Law Act 1975 (Cth) governs the way in which parents decide on custody arrangements in Australia. Generally speaking, parents may come to any arrangement for the care of the child a that they see fit, so long as both parents are happy with the arrangement and consent to it, and the child is safe and healthy. It appears as though this is what you have done up until now with your children. Usually when parents come to an arrangement that suits them they will apply to the Family Court for approval. An order by the Court to this effect says that their arrangement is satisfactory, and from that point on it can be enforced by the Court.

You wish to take your daughter overseas, however her father does not want her to leave. Under Australian family law a parent may not withhold access to a child from the other parent without their consent, this include the relocation of a child overseas without consent. When considering custody arrangements the Family Court will always consider the best interests of the child first. In Australia this includes the right of the child to see both parents. If one parent objects to the relocation of the child it is very unlikely that a Court would approve this.