The woman has asked the Department of Foreign Affairs to revoke his diplomatic privileges and have him declared persona non grata to stop him fleeing the country with their children.

The envoy's ambassador has refused to withdraw his legal immunity despite serious allegations of criminal conduct.

The diplomat, who was set to redeployed later this year, may have had his departure accelerated and will leave Australia before the end of the month.

The envoy allegedly told his wife he planned to take their children with him.

The woman has asked the Family Court to order the children be placed on a watch list to prevent the man from removing them from the country.

She has also asked he be ordered to surrender the children's passports, and be restrained from obtaining new passports for them.

But the man has refused to submit to the court's jurisdiction.

The matter was adjourned on Thursday until April to discuss the issue of jurisdiction, so the matter could await DFAT's decision on whether to revoke his diplomatic privileges.

The family has been living in Australia on diplomatic visas since 2010.

The parents separated in April and take turns to care for their children.

But the mother claims after the split the man grabbed her by the throat, threatened to kill her and her new partner, broke into her home, took her car, and gained access to her email and phone.

In one email to the woman, he allegedly wrote: "The police do not exist for me because I am a diplomat."

In an affidavit filed in the court, the woman said, in 2014, the diplomat would enter her home without permission to check her emails and phone records.

He allegedly threatened to kill her, said he would like to "put a bullet" in her new partner's head, and grabbed her throat in the presence of the children.

The diplomat allegedly became upset when she said she and the children would not relocate for his next posting, instead choosing to stay in Australia.

Earlier this month, she says he took her car without her permission and the following day came around to her home, knocked and kicked on the door, before breaking a window to gain access to the property.

She ran outside, they struggled, and he took a mobile phone.

He then sent her an email saying: "You will die on the street alone. You will have no money. Never contact me again. Only contact me about the children. The police do not exist for me because I am a diplomat."

Australian Federal Police's Protective Services spoke to the man, who said he would pay for the broken window and return a remote for the garage door.

Documents from the federal police, viewed by the woman's lawyers on Thursday, appeared to support the affidavit, although the court suppressed the contents.

The affidavit also said the man had commenced divorce proceedings and the sale of their property in Europe.

Family law solicitor Denis Farrar told the court during last week's hearing that it had been outrageous for a diplomat to hide behind immunity to behave in a manner the wife alleges is criminal and contrary to the interests of the children.

Mr Farrar, a former ACT Law Society president, said the embassy had permitted it to occur by preventing the court from taking action.

"These cases are rare but when they happen the interests of justice and the children come second to the immunity of diplomats," Mr Farrer said.