You can get an order through the courts which will make her stay!
It would be more correct to say: You MAY get an order which would stop the child being taken abroad. I would suggest that you immediately consider initiating court action if the other parent has threatened you with zero time. The existence or not of current court orders would be significant in what actions you should take. Could you say whether you currently have orders and if so how long they have existed for. What ages are the children?
You could also consider protecting the child from being removed. You may find the following useful (note! if you are in WA then things will be a little different):
Family Law Courts - Relocation and Travel said
How can I prevent a child from leaving Australia?
If you are concerned that a child may leave Australia without your permission, you should seek legal advice as soon as possible.
You can apply to the Court for an order that:
prevents a passport being issued for a child requires a person to deliver a childs or accompanying adults passport to the Court, or prevents a child from leaving Australia. (a) Preventing a childs passport being issued
If you want to prevent an Australian passport being issued for a child, you can:
lodge a Child Alert Request at any Australian Passport Office, or apply to the Court for a child alert order.
A Child Alert Request warns the Department of Foreign Affairs and Trade that a person may apply for an Australian passport for a child without proper and legal consent. If a child alert is in force and an application for an Australian passport is received for a child, you will be notified by the Department of Foreign Affairs and Trade.
A child alert request made at an Australian Passport Office is valid for 12 months. A court ordered child alert stays in force until a child turns 18, or as directed by the Court.
Note: A child alert does not stop a child departing Australia on a valid Australian or foreign passport, and does not cover passports issued by other countries. If you think a passport may be issued for a child in another country, contact the embassy of that country.
For more information about child alerts, contact the Australian Passport Information Service on 13 12 32 or go to www.passports.gov.au.
(b) Delivery of a passport to the Court
If there is a possibility or threat that a child may be removed from Australia on a current passport, you can apply to the Court for orders. The Court may order the delivery of a childs or accompanying adults passport to the Court. If ordered, the person in possession of the childs passport must deliver it to the Court. The Court will keep it for the specific amount of time detailed in the court order or until further order of the Court.
If there is a possibility or threat that a child may be removed from Australia, the Court can make orders which:
restrain the removal of the child from Australia request that the Australian Federal Police (AFP) place the childs name on the Airport Watch List, and request that the AFP assist in the implementation of the order/s.
The AFP will need a copy of the court order before placing a childs name on the list. The childs name will stay on the Airport Watch List until further order of the Court.
Note: If you consent to a child travelling out of Australia in the future or wish to take a child out of Australia yourself, you must apply to the Court (before you travel) to have the childs name removed from the Airport Watch List. If you fail to do so, a child may be prevented from leaving irrespective of who they are travelling with. The AFP cannot remove the childs name from the list without an order of the Court.
The AFP has offices in each capital city and some regional locations. Go to www.afp.gov.au or look in the White Pages for contact details.
What if the Court is not open when I need to make an urgent application?
The Court has an out-of-hours service for emergencies: that is, there is a risk that a child may be taken out of the country before the next working day. Call the courts on 1300 352 000 out of business hours and you will be referred to this emergency number.