The incident sparked a 20-minute row at a Sainsbury's store in Luton, Bedfordshire after Claire Ramscar to back down.
Ramscar said: "I followed this car into the car park and watched him pull into the parent and child bay ahead of me.
"He clearly didn't have any kids so I just sat behind him. I had two young children with me and I wasn't blocking anyone else."
The married marketing executive said she was tired of customers "abusing the system" at the store and vowed never to shop there again after claiming bosses backed the other driver.
Ramscar continued: "I asked him what he was doing and he just told me to shut up and walked off. I flipped, I'm not proud of it, but I just left the car where it was.
"I went straight to the customer service desk and gave them the registration number.
"They took my details and the next I heard from them was over the speakers asking me to move. I couldn't believe it.
"I spoke to staff and asked them why they didn't enforce their own rules, but they were making the whole thing out to be my fault."
Ramscar went into the store for lunch with her mum and her two daughters, aged three and 15 months, and kept an eye on her silver Citron DS5 from the cafe.
She eventually relented and left the store after her daughters became upset.
Ramscar said: "The guy had the cheek to claim that he'd (dropped) someone off with their kids, but I followed him the whole way in.
"It's incredibly annoying for people with young kids who need those spaces to have someone swan in and abuse the system like that.
"I'm not looking for special treatment. We used to have a disabled badge because one of my daughters was ill but we gave it back because we no longer needed it.
"It was the attitude of the guy and the store's refusal to ask him to move that annoyed me more.
"I can't remember his exact words but he said something that infuriated me and changed my mind about moving.
"But then the girls were getting agitated so I decided it would just be better to leave.
"Everyone was looking out the cafe window because they could see him getting frustrated and I wanted to check he wouldn't damage my car.
"I go out of my way to go to that store but I won't be back."
Sainsbury's Bramingham Park store has 378 parking spaces, with a further 18 for blue badge holders and 12 parent and child parking bays.
Sainsbury's claim they asked Ramscar to move her car because it was blocking the car park.
Their policy is to ask someone parked incorrectly in a parent and toddler bay to move and issue a ticket if they do not however they cannot guarantee that all incidents will be spotted immediately.
A Sainsbury's spokesperson said: "We monitor our car parks closely for parking violations. Customers are invited to contact a colleague if they notice that someone has parked incorrectly."
When Ramscar posted the picture on her Facebook page, other social media users were divided over whether she was right to take matters into her own hands.
Adam Crofts said: "What if this person was there to pick up his wife and kids? No matter what the reason you can not take break the law to teach someone a lesson. What if this person were disabled and all the disabled parking was gone?"
While Lindsey Norman said: "Ok, so, he hasn't got children in the car, fine, could park somewhere else BUT he was parked in a designated parking space and you were not, the manager was well within his rights to tell you to move!
"I understand your frustration though and it is a squeeze to get little ones out without a bit of room! Verbal abuse was not needed, especially as I assume you had your children with you! Naughty man for being mean, naughty lady for parking in a non-designated space!"
Rosalind Tomlinson said: "I think Claire was trying to make the point that people park in the parent and child place when they don't have children, I know it isn't law but it would have been polite of the driver to move when he could see Claire had two small children."
And Beverley Allen praised the mother: "Good for you doing this! Also people without kids... don't you realise that you need extra space to get your children in and out of the car so these spaces help parents do this without hitting other cars with the doors whilst trying to squeeze your kids in the little gap you get in normal spaces. I would've blocked their car in too!"