An advocate for the family, Sue O'Callaghan, said doctors initially failed to recognise that the first child had a rare genetic condition known as osteogenesis imperfecta, or brittle bone disease - a diagnosis finally made on August 19 when the girl was found to have "a novel mutation consistent with Type 1 osteogenesis imperfecta".
O'Callaghan said, in her view: "We are stuck in a situation of medical negligence.
"I spoke to consultants in America who said because the child was diagnosed with Type 1, most breaks happen in the first six weeks and all breaks are unexplained.
"The child can break ribs through coughing. The Osteogenesis Imperfecta Foundation stipulate very clearly that broken ribs are very normal with Type 1 babies."
Former Race Relations Commissioner Joris de Bres has also met the family and read all their medical and official records, and has asked Oranga Tamariki chief executive Gráinne Moss to review the case. De Bres and his wife have two daughters and a grandson with brittle bone disease.
He said he had "absolutely no sense" that either of the parents were bad parents.
"My feeling is that the injury is very plausibly explained by the condition that was not diagnosed until later this year."
About one in every 20,000 babies are born with brittle bone disease.
The author of a recent review paper on the condition, Professor Tim Cundy of Auckland University, said distinguishing between child abuse and brittle bone disease was "often problematic".
A spokesman for Oranga Tamariki said the ministry relied on "advice from medical experts".
"If specialists believe that injuries are non-accidental, then Oranga Tamariki's role and legal mandate is to act in the best interests of the child," he said.
"Ultimately it will be the Family Court who will consider all of the specialist medical evidence and social work assessments to make decisions around placing children in care."
De Bres said both parents in this case were from overseas.
"They are a young couple, they are low-income, they are migrants. It's not a good start in terms of fighting the establishment," he said.
"What's happened is that they [officials] have begun increasingly to question the mental state of the parents - but they have only ever known the parents since they have had something happen that would stress anybody.
"The mother had a seizure in her childhood, which has partly affected her ability to speak but I found her to be perfectly capable of communicating and reasoning.
"There is an incident they [officials] describe as saying the father has a violent tendency because in the middle of things at [the] hospital, where all this was happening, he went outside and punched a tree and partly injured his hand.
"I was thinking, well that's a very sensible thing to do, it's better than being violent to any human being, but that has kind of lived on in the story since then."
The couple are raising money online for legal costs to try to get their children back.
