The couple also said; the ambulance that took their daughter Lillie to the hospital did not have pediatric oxygen masks and the adult mask kept slipping off Lillie's face, there was a delay in them being told their daughter had died; no autopsy appeared to have taken place in spite of assurances in the ongoing trial that this had been done.
"It's time to face up to the reality. We don't want any other family to suffer the way we did. If you can't evacuate a mall and you can't handle an incident that affects 19 people, how is the health system there going to deal with an incident at an airport or a stadium?" Mr Weekes said.
The Joint Commission International, a healthcare accrediting body, is now investigating the hospital.
The complaint had the potential to "do serious damage to HMC's reputation as one of the region's premiere healthcare providers", said commission officials.
David Astley, group chief at the hospital, responded to the Weekes' letter last July, apologising for their experience, saying "this was the first incident of its kind here", and it had started a "lengthy investigative and learning exercise", Doha News said.
The Weekes family said they are still waiting for further communication more than six months later.
In a report New Zealand National Examiner in Embalming Gavin Murphy, who was commissioned by the Weekes to examine the children's bodies, said he was surprised to see that there were no identifying points indicating the children had been embalmed.
"Relying on refrigeration alone for preservation does require more luck than process and skill."
"We were extremely disappointed with the quality of care the three children received in Qatar. As a minimum, arterial embalming should have taken place to ensure maximum preservation," he wrote.
He also found no obvious signs autopsies had taken place.