The 32-year-old allegedly had a breath-alcohol level of 741mcg, nearly twice the legal limit of 400mcg.
Police would not release the ages of her child or the teenagers.
Senior Sergeant Richard Whitmore, of Balclutha, said it was alarming the woman had four young people in her car while driving in these circumstances.
"It's very concerning that the driver put the lives of young people, including her young child, at risk.
"The police will forward the matter on to Child Youth and Family for follow-up inquiries."
Police stopped the woman on Needle St, Kaitangata, and suspended her driver's licence for 28 days. She is due to appear in the Balclutha District Court on May 30.
The incident follows an operation by Balclutha police on Friday and Saturday nights, targeting repeat drink-drivers.
An 18-year-old man was caught with an alleged breath-alcohol level of 217mcg - the legal level for a person aged under 20 is 150mcg.
Snr Sgt Whitmore said police also issued a large number of infringement notices for breaches of driver's licences.
Outside of the operation, a 26-year-old woman was charged with driving with a breath-alcohol level of 559mcg, he said.
