No, it is not appropriate at all. Such a story involves disrespect and improper behavior towards family relationships. Family relationships should be based on love, respect and positive interactions.
Maybe it's from a group of people who have a very strange and boundary - pushing idea of what is comical. They might come up with such ideas without considering the inappropriateness and how it goes against normal family values. It could also be a result of trying to create the most out - there and 'edgy' content, but it's really not acceptable in proper society.
By having good moral and ethical values. We should know what is proper and improper in family relationships and avoid creating or sharing any content that might violate family respect.
I highly doubt there are real such stories in a normal or appropriate context. This kind of description seems rather inappropriate and unhygienic. It's not something that should be part of a normal family or social narrative.
Imagine a mom driving her kids to school. She steps on the gas a bit too hard and farts. The kids start teasing her, but she tells them that it's just the car making a strange noise. They keep arguing about it all the way to school, and by the time they arrive, they're all in a good mood from the silly conversation.
There was this mom in my neighborhood. She was chasing her naughty kid in the park. While running, she farted a bit. Her kid turned around and said 'Mom, what was that?' She just blushed and said 'Oh, it's just my body's little joke'. Later, she told the story to other moms and they all had a good laugh.
Since I don't know the actual story, it's hard to say if there's a moral. However, if it's a humorous story, the moral might be not to take small, embarrassing things too seriously.
Once there was a mom who decided to start doing yoga to keep fit. One day during a particularly intense yoga session at home, she accidentally let out a fart. She was so embarrassed as her kids were in the next room. But then she just laughed it off and continued with her poses, realizing that such things can happen to anyone during physical activities.
There isn't enough information here to accurately tell the story. It might be from a particular book, show, or someone's personal creation. If it's from a show like 'Dexter's Laboratory', there's no such well - known plot about his mom farts in the mainstream episodes.
There could be a story where a child misinterprets the sound of a mom sneezing as 'face farts' and then it leads to a series of comical misunderstandings in the family. For example, the child keeps asking the mom if her face is okay because it 'farts', and the mom is initially confused but then finds it hilarious.