Ms Biugos was offered a Housing NZ house in Flaxmere, Hawkes Bay, but declined it as she said the move to a strange town would have been too unsettling to her children.
She was also matched to another property in Auckland but the property was never formally offered to her.
"The place in Flaxmere was not just moving us into a new town, it was in a rough area with known gang houses.
"They are moving Aucklanders into Tauranga state houses and asking us to move out of town.
"I don't think it is fair and I don't know how I am going to pay the money.
"I do want to get a job but it is hard when you haven't got a permanent address, but when I do have an address I will work.
"My son would not have coped well, and that was the opinion of those who care for him too. I have no family or support there."
Housing NZ said it accepted her reasons for declining the home but advised her that it might meant that she would have to pay for future motel stays.
Ms Biugos said constantly moving between motels was difficult for the children.
"Anyone with kids knows how hard it is for them to be crammed in a small space..in the motels there was nowhere outside for them to play and I tried to keep them quiet to be mindful of other guests.
"It is particularly hard on my son with autism as he needs stability and all the moving around has been really unsettling."
Kay Read, associate deputy chief executive social housing, said staying in a motel for long stretches was less than ideal for anyone.
"That's why it's so pleasing to see that we've been able to help the family move into, and pay for, their private summer rental," she said.
Ms Read said the agency would continue to try to help Ms Biugos find a housing solution, but it was going to be challenging.
"The reality is there just aren't that many available places with four or more bedrooms in the areas which Ms Biugos has told us she would be willing to consider...We'll continue to do all we can to help Ms Biugos and her family find somewhere to live long-term."
Ms Biugos suspected landlords were put off by the number of children she had,
Roger Barclay, owner of the Ambassador Motor Inn Tauranga, said he sympathised with Ms Biugos but rooms had been pre-booked for the busy Christmas season.
"From December we are pre booked out, with people who have already paid deposits or have given a credit card to hold the room - so it is hard on the families like Natasha's we have had staying as emergency accommodation as they cannot pre book the rooms which means they have to move out for Christmas."
