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Deborah Wai Kapohe said she and husband Michael Beazley, together with their two children, had built the nest inside a downstairs living space.
The room was "like being in a student flat", but the family were determined to remain in their home until the Weathertight Homes Resolution Service (WHRS) mediation process was completed, even though that might take until Christmas, she said.
"We're trying to make ourselves as small a space as we can that we can still heat. It's freezing cold... I've had three jerseys on and I've had to cook in a hat and a coat," she said.
The family learned in April their $550,000 house in Glenleith had been officially declared a leaky home following an inspection by a WHRS assessor earlier this year.
The results showed their home was in need of full recladding, but exactly who would pay for the repairs was yet to be determined.
The couple bought their home late last year, after checking it had a code of compliance certificate issued by the council, but discovered the first signs of cracks, leaks, toxic mould and other faults days after moving in.
Mayor Dave Cull has indicated the council would work through the WHRS process with the family, and, if found to be liable, "would meet that liability".
Ms Wai Kapohe said the next step was to prepare an application for the WHRS mediation process, which required information from other parties and could take two months.
Once completed, the application would lead to teleconferences, mediation and, if parties couldn't agree, an adjudication process, she said.