She and her mother flew over from their home in Matamata for the treatment in September, and the rest of the family joined them on December 18 to stay over Christmas, after gaining emergency allocations in a managed isolation facility from December 30.
However, Kate's health began to deteriorate recently and she has been placed in the Paediatric Intensive Care Unit (PICU).
The family applied for an extension to their MIQ application for Marc, Fletcher and Jessie, so they could stay on for another few weeks until she had stabilised.
However, this was declined. As was their application to self-isolate at home.
Speaking to the Herald on Tuesday morning, Jackie said they were just hoping to extend their stay until Kate's condition had improved.
"The main thing we are worried about is that they can't leave isolation in those two weeks, if anything happens."
Following inquiries from the Herald today, and MIQ spokesman said they discovered an error in the application process and had since reversed the decision.
"We are very sympathetic to the situation this family is facing during this global pandemic," the spokesman said.
The family had originally been granted an emergency allocation on December 15 to quarantine in a New Zealand managed isolation facility on the December 30.
"At the time this emergency allocation application did not meet any of the categories, but was approved under extraordinary circumstances at the discretion of a senior MBIE approver," the spokesman said.
However, when the family submitted a new emergency allocation request, the person assessing this second request was not aware the case had previously been approved under the extraordinary circumstances criteria.
"Without this crucial information included, it did not meet the emergency allocations criteria and the application was declined," the spokesman said,
"Upon reviewing this case, this emergency allocation has been approved under extraordinary circumstances and the family have been notified.
"On behalf of MBIE we wish the family well and apologise for any additional stress incurred as part of this process.
"We have requested a case review to minimise the chance of this happening again."
Speaking earlier in the day, Jackie said the family was grateful to be in Australia for the specialist therapy in the first place, funded through the Ministry of Health.
But having family there at this time was making a huge difference.
"It is amazing to be here, and we are very grateful, especially to be able to come over in a pandemic. We just want to thank everyone for their support."
