Sinead Heritage, of Wharf Lane, Solihull, was arrested after the Vauxhall Astra she was driving hit a BMW on the same street, on July 13 last year but she had failed to stop and give her details.
Solihull Magistrates Court also heard that she had been driving without insurance or a valid driving license.
Heritage told Magistrates she had only got behind the wheel to get medicine for her children.
“My kids were ill, one of my children is autistic,” she said. “Their father was off doing his own thing.
“I was left in the house with no medicine.”
Malcolm Stoddart, prosecuting, said the children, aged nine months and three years, had been in the car at the time of the accident.
Heritage had eight points put on her driving record and was ordered to pay £495 in fines and costs.