"I've been going to viewings of properties where there were easily another 30-odd people looking," Smaling said.
"We are now on ACC and a benefit, and it became a refrain that 'this is [for] a professional working couple.'
"Also with the kids' bone condition and his [Runciman's] current situation, we can't have two-storey homes. Falling down stairs is a huge risk for broken bones."
The family also needs to be close to Palmerston North Hospital.
Smaling has applied for a four-bedroom social housing unit but said Work and Income had told her "it could be three to six months if we're lucky" before a suitable home became available.
The family contacted the Herald after another family with brittle bone disease had their two children, including a newborn baby, taken by CYF's replacement the Ministry for Vulnerable Children Oranga Tamariki because of suspected child abuse.
Smaling said her family never lost a child because Emma's brittle bones condition was diagnosed when bone fractures were picked up on scans before she was born.
Runciman's brittle bones had also been picked up when he was 15 by a visiting doctor who noticed the telltale sign of blue veins showing in the eyes, so the genetic condition was known to be in the family.
Nevertheless, CYF was called in every time Emma or LJ broke a bone for the first three years.
"On one of the first two or three visits they actually said I had made this up [brittle bones disease] to cover up the child abuse," Smaling said.
"It was after receiving numerous letters from paediatricians and specialists when they said this isn't made up, and they backed off.
"But they still had to come back and check because there were allegations of child abuse. It got to the point where they had been so often that they would say, 'Hi, how are you,' and they would leave.
"They probably came a good 20 or 30 times. They stopped when my daughter was about 3 years old."
Palmerston North has not had a housing shortage until recently. Manawatu-Whanganui's population declined from 1996 to 2002 and then was stable until 2013, but increased by 5700 in the three years to June last year with the reversal of the previous outflow of New Zealanders to Australia.
Manawatu Tenants Union co-ordinator Kevin Reilly said the local housing shortage had worsened in the past three to four years, partly because Housing NZ had demolished some state houses. He said the agency used to have 1500 state houses in the city but latest data shows the number has fallen from 1454 in September 2015 to 1433 this June.
Conversely, the city's social housing waiting list (excluding transfers) has ballooned from 16 in June 2015 to 148.
"I've never known it to be as bad as this," Reilly said.
Ministry of Social Development regional manager Justin Wilson said Work and Income met Smaling on Monday to discuss the family's housing options.
"It is always difficult to say how long it will take to find a suitable home because there are many factors to take into account, especially given in this case the family needs to be near a hospital and school," he said.
"However, this family's priority rating has risen as their circumstances have changed."