"The doors squeezed together on the pram, so contrary to popular belief they are not like elevator doors, they don't open again, and the train started to move.
"The conductor who was standing right next to me, all she could do was say sorry. She did nothing else. She could not stop the train, she did not raise any alarms.
"The girls ran down the platform crying after the train and that was the last I saw of them."
Chelsea and Zara were left stranded on the platform, while Peterson and Georgia carried on to Porirua.
Peterson said a member of the public offered to drive her back to Paremata after seeing what had happened.
"I was pretty distraught, very, very concerned about their safety.
She said she had no idea whether the girls had stopped running after the train left the platform, or whether they had tripped or fallen down.
"It's bad enough when you're standing there as a mother with kids on the platform, telling them to stay behind the line so they're not in a dangerous position.
"Who's going to tell them that when there's nobody with them?
"Luckily when I got back there, a man called Richard who was lovely had found them and stayed with them."
She said she wanted to send a huge thank-you to Richard, and to Darryl who drove her back from Porirua.
Peterson said Transdev, the company that operates the trains, had called her today.
"They rang to apologise, but they couldn't go into specifics because it's to be investigated.
"The man said the train staff were new, but to be honest that's not really my problem, they should be trained if they're new - if anything, they'd have the latest training."
She said she wanted to know why an emergency alarm was not raised to make the train driver to stop.
Peterson said her daughters are "fragile" today, and are going to take a lot of convincing to get back on a train.
Transdev had launched a full investigation.
A spokesperson from Transdev said, "Senior management are involved with this investigation, which includes onboard service, security and training."
They said an emergency stop lever should have been used.