Hello my sister has just found out her husband has been unfaithfull…

HiCustomer
as the child has a passport and I assume is a citizen of Northern Ireland she doe snot require her parents to consent to her travels and entry into Northern Ireland, as she is a citizen.
If the father discovers that they have booked tickets he can put on an urgent application with the family court and have them stopped at the Australian Border and they will not be permitted to board the flight.
Even if she manages to go to Northern Ireland I would assume the father will file an application for the child to be returned. The court both here and in Northern Ireland will not be very impressed with the mother taking the child without the fathers knowledge.
The law in Australia looks at what is in the childs best interests not the parents. It is always best for the child to spend time with both parents and get to know them.
It is difficult and she is in a difficult situation.
In Australia for childrens matters you need to seek mediation before you can go to court. If she notifies him that she is going to go back to Northern Ireland he may file an application to stop that happening. Bit if it is best for the child to go back to Northern Ireland the court will make the order.
You should contact your closest family relationship centre. This is a free service provided by the Federal Government. Their website is
http://www.familyrelationships.gov.au
You can find your closest one on there.

The web-site also have alot of useful information and links to assist you.

Before going to court you must obtain a certificate from a family dispute resolution practitioner. You get this through the free service provided at the family relationship centres.

If you need to go to court then you can will need to file an application in the Family Court or the Federal Magistrates Court
http://www.familycourt.gov.au and http://www.fmc.gov.au
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