They had two children together while living in the United States, and their third was born after they relocated to New Zealand.
The necessary paperwork for Ms Cifuentes to become a New Zealand resident was not completed during the couple's marriage.
She was on a partnership work visa, which was renewed every two years.
However, since the separation, she was not permitted to work because she no longer had partnership status and for the past eight months had been here on a visitor's visa only, she said.
After having an application for another work visa turned down, she enlisted the help of Waitaki MP Jacqui Dean.
Mrs Dean said she had been working directly with the Associate Minister of Immigration's office to seek an exemption for Ms Cifuentes.
Associate Immigration Minister Nikki Kaye has the responsibility of reviewing individual cases and overruling earlier decisions. She was still considering Ms Cifuentes' case, and had requested further information, a spokeswoman from her office said.
However, Ms Cifuentes said she was tired of fighting with only limited resources to stay in New Zealand.
"I've been doing this for two years ... I'm done.
"There comes a time when you have to stop the battle."
She was now resigned to leaving and focused on finding a way to take her children with her, as she said she did not have Mr Nolet's consent to do so.
She planned to make a court application for the removal of the children from New Zealand.
Lawyer Graham Hill, who has been working pro bono on Ms Cifuentes case, described it as a "tragic situation".
"I'm appalled that a family could be busted up like this because of immigration," he said.
"In terms of the immigration policy there is a gap, a hole in the policy. It doesn't recognise the interests of New Zealand children to have their mother with them which is a fundamental human right ... therefore the Minister should exercise her discretion to give Sisi status."
Despite Ms Cifuentes' prolonged efforts to stay in New Zealand, her lack of income made leaving inevitable, Mr Hill said.
"As soon as she left the matrimonial home her status changed. She wasn't eligible to work and she's on a visitor's permit, so she wasn't entitled to a benefit."
Ms Cifuentes had depleted her resources to the point where leaving was the preferable option, Mr Hill said.
An Immigration New Zealand spokesman said it was not possible for foreign nationals to apply for residence in cases where a partnership has broken down and the couple were no longer living together.
The Otago Daily Times made repeated attempts over several days to contact Mr Nolet for comment, but has been unable to do so.
