In general, the prejudice that women can't drive well is common. Are there single words or phrases belittling female drivers in Korean?
I think the word you're looking for is '김여사' which translates into 'Madame Kim'. It's a derogatory term for bad female driver.
Kim is the most common last name in Korea and '여사' is a formal title often used for someone with higher education or wealth.
Basically, stereotyping upper class people who have chauffeurs, or who get their driver's license via bribery, etc. that don't know how to drive.
Here's an example of video post with the term used in the title
Google for more examples.
I don't think there is a particular word to describe a woman who can't drive well. However, you can hear people say
왜 너는 아줌마처럼 (아줌마같이) 운전하냐? Why are you driving like a middle-aged woman?
(1) when you are sitting too close to the wheel, (2) you can't overtake other cars very well, (3) when you don't park your car nicely, etc.
'아줌마' is a disrespectful word for '아주머니' and it is used in a variety of context to be scornful or sarcastic when people show an unbecoming behavior or appearance.