The company spokesman added: "No children exited the vehicle and therefore the driver did not require the extra space provided and should have parked in a regular parking bay."
Rachel, from Cringleford, Norfolk, said: "I feel so annoyed. It's just an easy way of making money out of people.
"I just saw a parents' space and parked there. I thought that will do, my boy's not well and I need to get in and get home.
"There's no leeway and no humanity. With three children, that's a lot of money for 20 minutes' parking."
She justifies leaving her poorly three-year-old Benjamin with older sisters Sofia, aged 10, and Amalia, aged seven, while she popped into the shop.
The National Parking Enforcement (NPE), which manages the car park, issued her a parking charge notice (PCN) requesting that she paid a £100 fine.
She also received a mother PCN but because she did not check the dates she assumed that they were for the same incident.
Her appeal for the fine was turned down and she was then charged and £60 for debt recovery fees for failing to pay the second fine.
She said: "I didn't even know it was against the rules to leave your kids in the car in a parents' parking space.
"I went back and read the small print on the sign and it did say you've got to be accompanied out of the vehicle by a child under the age of 12. I admit I didn't see that.
"But the photos they sent me of my car in the space showed two other free parents' spaces.