"Due to her driving and her demeanour, she was taken to the Hastings Police Station, where she was processed for drink-driving," Mr Clinton said.
"She refused to have a blood sample taken."
The woman is due to appear in Hastings District Court next Wednesday, charged with refusing to give a blood sample and dangerous driving.
Mr Clinton said the incident, which had left officers "dumbfounded and angry", was particularly disturbing in light of recent publicity for Road Safety Week this week, with a particular focus on Hawke's Bay schools.
Checkpoints had been set up outside some schools and arterial routes, with police checking on seatbelt wearing, cellphone use and enforcing the 20km/h speed limit past stationary school buses.
"This incident just highlights the unknown dangers on our roads."
"Not only did this woman put her own children at risk, she also put other road users at extreme risk of injury or even death.
"It was totally irresponsible and dangerous."
Mothers Against Impaired Driving (MAID) spokeswoman Linda Anderson said the incident was "extremely concerning".
"It's absolutely disappointing someone could do such a thing."
She said a child's parent or caregiver was required by law to ensure the child had a correctly fitted and age-appropriate restraint.
In response to the incident, Tukituki MP and Associate Transport Minister Craig Foss urged drivers to be vigilant on roads.
"Any accident on our roads is disappointing, especially during Road Safety Week which is focused on keeping our children safe," he said.
"I urge everyone to please take care on our roads to keep our families safe."