She was arrested and charged with drink driving, careless driving and two charges of ill treatment of a child under 18.
The woman's lawyer, Ashooja Chandra, said a pre-sentence report reinforced the woman's remorse and that her actions were out of character.
"It's my submission that [offender] acted completely out of character for her. It was a time in her life which amounted to extenuating circumstances.
"She was coming out of a domestic violence situation. She was in the women's refuge for some time, she had a lot of stress on her and it resulted in a poor choice that she made on that day."
The woman had not drunk any alcohol since getting arrested.
"She is deeply regretful that she placed her children in that position ... her children are doing well in school otherwise and it's not a situation that will be repeated again," she said.
Judge Connell accepted the woman's position and said he needed to impose some punitive element to run alongside a sentence of supervision to be consistent with others who offended in a similar way.
"The worst aspect of it is the risk to her own kids at the time she was driving, that's the thing that worries me," he told Chandra.
"I don't want to be too harsh in terms of her circumstances ... but there needs to be some punitive element."
The judge told her he could understand her resorting to alcohol after what she had been through as she might have thought it would ease her pain, but getting behind the wheel was the wrong option.
"I'm fully sympathetic to those circumstances ... being physically abused.
"It puts you in a position where I can understand your depression and your resorting to alcohol. I don't understand why, when your'e like that, you then decide to get in your car and drive with your kids."
He convicted the woman on all charges and sentenced her to 60 hours' community work and 12 months' supervision.
The solo mum was disqualified from driving for three months but after 28 days she can apply for an alcohol interlock licence which will last for a year.
Alcohol interlock licenses became mandatory from July 1 this year for serious or repeat offenders.
After 12 months, she will then have to apply for a zero alcohol licence.
"I don't expect to see you back here. You look at particularly the success your kids have achieved at school. It's a sign they have been well looked after by you and I think you should be allowed to continue the same process with them."
She had also earlier completed an alcohol impairment programme.
