Hey there! Daughter of a BPD mom who displays many Narcissistic traits. I know it's not exactly the same as what you are describing, but I can offer some insight as to how my mom treats me and my siblings.
I was often treated as the family scapegoat, being blamed for everything. My mom had this idea in her head that I was a bully towards my youngest sibling, when it was actually the other way around. She would pit us against each other, encouraging my siblings to insult me or snub me or sometimes physically hurt me. I had to do all the chores, and would sometimes be woken up in the middle of the night to go sleep next to the dog's crate, or wash the floor on my hands and knees. If ever I complained, she would unleash her fury and she'd tell me how ungrateful I am and that she's an awesome mother, and that she always does everything and that I'm just a lazy good for nothing (important note: in addition to constant cleaning I was doing well at school and played competitive sports). She limited my socialization as punishment when I "disobeyed" her, or didn't do something "right", and as a result I had very few friends. My siblings weren't treated like this, but I don't think they had it much easier. The middle sister was the favorite, my mom was always talking about how great she was and how pretty and how successful and would dote on her. She idealized my sister. However, this put a ton of pressure on her to be everything my mom expected. Which isn't easy. My mom saw her as an extension of herself, and wanted my sister to be a mini-her. Any individuality or deviation was met with guilt trips and punishments and yelling.
Now that I'm an adult and no longer live at home, she has resorted to using guilt to control me. It's very effective. She tries to control everything I do and wants to monopolize all my holidays or special occasions, otherwise she takes it as proof that I don't care about her. I live 6 hours away. I am definitely the most fragile of my siblings today. The "favorite" has managed to build up a thick skin and resists my mom's attempts at control quite easily. I'm proud to say we've gotten a lot closer since we all moved out.
It's a lot of drama and fear and rejection for the kids. My mom alienated me from almost all adults in my life who cared about me or wanted to help me. I imagine that having other adults in their lives who can model healthy behaviours and relationships would be incredibly beneficial.
Just my two cents.