No, it's not appropriate. In most cultures and for reasons of privacy and healthy boundaries, parents and children should have separate bathing times as children grow older.
I'm not sure specifically which 'shower with mom story' you are referring to. It could be a personal family anecdote about a shared shower experience perhaps for some practical reason like a small child being scared to shower alone and the mom being there for support.
No, it's not a very common type of story in general. Most family stories tend to be about vacations, holidays or special events. However, in some families where there are unique family dynamics or a need to share certain experiences for educational or emotional reasons, such a story might exist.
Since I don't know the exact 'mom shower curtain story', here's a possible one. Maybe the mom had an old, tattered shower curtain that she finally decided to replace. She took her kids to the store and they had a great time looking at all the different patterns and colors of shower curtains. In the end, they picked a bright and colorful one that made the bathroom look much more cheerful.
I'll share my mom's shower story. When my mom was on vacation at a beach house, the shower in the bathroom had a really strange water pressure. Sometimes it was too strong and would almost knock her over, and other times it was so weak that it took forever to rinse off the soap. But she still made the best of it and had a great time on that vacation despite the shower quirks.
A mom outdoor shower story could involve her using natural products during the shower. For instance, she might use a homemade soap made from local herbs. There could be a story about how she got the idea to do that. Also, the wildlife around could play a part. She might see a little bird or a butterfly while she's in the outdoor shower and it makes her day. Maybe she even has a little conversation with a neighbor who passes by and is curious about her outdoor shower setup.
Once, my mom had an interesting outdoor shower experience while we were camping. There was a small waterfall near our campsite. She decided to take a 'shower' under it. She was so excited, like a child. She wore her swimsuit and just let the water splash over her. It was a really refreshing moment for her.
Perhaps the story is about a mom who discovers a hidden world behind her old, tattered shower curtain. One day, while cleaning the bathroom, she notices a small tear in the curtain. When she peeks through it, she imagines a magical land filled with tiny fairies and talking animals, which inspires her to be more creative in her daily life.