Ms Cifuentes (43), who was born in Nicaragua, was due to fly to the United States next week, having failed to get another New Zealand work visa. Her visitor's visa was due to expire tomorrow.
She wants to take her three children with her, rather than leave them behind with their New Zealand father, international model Peter Nolet, from whom she is separated.
Ms Cifuentes' lawyer, Graham Hill, made an application for the removal of the children this week on behalf of his client. During a review of the parenting order at the Queenstown District Court yesterday, Judge Michael Turner gave timetabling directions for the application, Mr Hill said.
A list date of March 12 had been set down to review proceedings. However, there was no date yet for the application to be heard and ''it could be months before one is available'', Mr Hill said.
''It's an invidious position for an applicant to be in.''
Ms Cifuentes said she visited the Immigration New Zealand office yesterday while in Queenstown and was granted a two-month extension on her visitor's visa so she could attend the next court date.
She had also been able to change her March 6 flight to a later, yet-to-be-confirmed date.
''I'm going to stay to fight it,'' she said.