Sarah Herrod, 57, of High Street, admitted being in charge of the Vauxhall Mokka car when it was driven in Victoria Road in Skegness on September 9 and clipped a parked police car.
It was said she gave a breath sample of 45 microgrammes of alcohol, the legal limit being 35.
Mitigating, Asad Aziz said she had been unaware that she had been committing an offence.
Asking the magistrates not to disqualify her from driving, he said she needed the car, particularly as she had to take her disabled son to medical appointments.
Mrs Herrod, who had no previous convictions, was fined £80 and had 10 penalty points put on her licence and was ordered to pay a total of £119 in court costs and charges.