But landlord Satya Silan said the council had told him to evict the family by October because he did not get a building permit for the conversion and the concrete floor is only fractionally above ground level.
"A standard house has to be 15cm above the ground, which this does not comply with," he said.
Ioelu said she was living with her parents before she had her baby, but once the baby was born she and Mah Yen needed more space.
She has asked Work and Income for social housing and has been told to come back this week with proof of the family's finances and impending eviction.
"I can't go on the road, I can't go sleep in the car with my son, he's too young," she said.
Meanwhile several people who have recently been homeless are among 450 people who have made submissions to an inquiry on homelessness by the Labour, Green and Maori parties which opens at Te Puea Marae in Mangere Bridge tomorrow Monday.
Although National MPs refused to support the inquiry when it was proposed in Parliament's social services committee, National coalition partner Maori Party co-leader Marama Fox said her party supported it because addressing homelessness was her top priority in the Ministerial Committee on Poverty.
"New Zealanders in general are disturbed by the fact that we have a homelessness situation in this country. This is not the Aotearoa that we want to live in," she said.
Labour MP Phil Twyford said it was "profoundly shocking" that families with children, many of them in paid work, were living in cars and garages because they could not afford anywhere else.
Green MP Marama Davidson said: "The whole point is for the country to have a direct and clear understanding of what is actually happening to be able to move people enough that we collectively demand some change and some solutions."