She was in police custody last night and said to be "extremely upset".
Child, Youth and Family had been been called in to help the family four years ago but had no contact with them since then.
Regional director Southern Paula Attrill said: "The two children involved in this terrible incident are safe and are living with a family member.
"We are working closely with police as they continue their investigation."
Police have contacted the father of the two children.
On his OldFriends site, the father had said: "I have two beautiful kids and a wonderful partner who I plan on spending the rest of my life with."
But, according to a Facebook update, he has since moved to live on the Gold Coast. He could not be contacted last night.
Support groups urged single parents to seek professional help if they felt under pressure.
Sue McGuire, president of single parent support network group Birthright, said single parents often found that going through a separation was very traumatic. There was a stigma, some felt.
"Birthright is available as a support group and can help as an intermediary for accessing services like counselling or help with accommodation."
David Do, co-president of the New Zealand Union of Students' Associations, said students had come under increased strain since the recession.
"Students are under constant pressure, especially those with children," he said.
Police were yesterday conducting a scene investigation at the woman's home.
Residents said they saw around 10 police and ambulance staff.
Detective Sergeant Mark Keane said no one else was being sought in connection with the charges.