She took the children to a domestic violence shelter, applied for a family violence intervention order and soon after brought the children to New Zealand where they have lived with her parents since January.
But they are to return to Australia under court order on January 2.
The order follows an application by the father under provisions of the Hague Convention dealing with civil aspects of international child abduction.
The convention aims to stop inter-country child abductions.
If the courts find that the children were removed in breach of the other parent's custody rights, they are ordered to return unless it is accepted that would create a "grave risk" of harm or that it would otherwise place the children in an intolerable situation.
In this case, the Family Court ruled that removing the children was a breach of the father's parenting rights.
The Court of Appeal this month upheld that decision and ruled that allegations of grave risk "whether they be domestic violence, financial hardship, or physical or psychological harm," should be determined by a family court hearing in Australia.
In her letter to the PM, sent before the appeal, the woman said she was seeing more cases like hers and it seemed New Zealand courts were not giving weight to sections of the convention that were available when returning children would likely create an intolerable situation or grave risk.
"The thing is . . . everyone gets sent back. I come from an abusive relationship where my children and I had nothing and will have nothing if we get made to return."
"It is so distressing that the Hague Convention allows sections for intolerable situations and grave risk as a factor of non-return, but I see no evidence that New Zealand is prepared to honour these sections."
The woman said she has no savings and, as a New Zealander, would receive much less welfare support in Australia.
She had been told by a law firm in Australia that the legal process of applying to relocate to New Zealand would cost at least $100,000 and take up to five years. She does not believe she will be entitled to legal aid.
The woman said the father had told the court that she and the children could live rent-free at a property they jointly own. However, she said, it appeared he had not been working and the mortgage was $20,000 in arrears.
She did not know anyone other than her estranged partner's family and might have to go to a women's shelter.
In her appeal, the woman argued that the lower court failed to take into account her ex-partner's alleged methamphetamine use, that his refusal to provide a hair follicle test which could have proved his drug use should have amounted to grave risk of harm.
The appeal decision notes that the father denies allegations he had been violent. It also refers to him having lost a job in 2014 after failing a workplace drug test.
Also noted is a voluntary acknowledgement by the mother that she had used drugs in the past.
The mother's lawyer, Murray Cochrane said in the vast majority of Hague Convention cases, New Zealand courts send the parent and children back for the courts in that country to sort out details such as access, custody and protection.
Cochrane said the great problem for people in his client's situation was the financial disadvantage New Zealanders face in Australia.
Although sent back by court order she won't as a New Zealander receive enough to live on, he said.
"It is the money to live on that is the big problem over there."
If his client was an Australian forced by court order to return to New Zealand they would be entitled to a special benefit.
"That is the ultimate irony, in my view."
Cochrane suggested the situations warranted discussion between the two governments about "why we are so generous and they are so niggardly".
His client and the children were flying into a distressing and uncertain situation.
"She won't know until she gets there whether she can move into the house."
