What do you think is normal? If you're questioning, then you must have an idea, yes? Leave It To Beaver? The Brady Bunch? Family Ties or The Cosby Show? Maybe it's just what you saw in other families. I was drawn to the family of my BFF bother from another mother. Nuclear family with a boy and a girl.
I did, however, know that the mother's often hour long yelling sessions at her husband weren't normal. She divorced him only a few years after I knew them.
Decades later, I found out that the dad suffered from depression. I also found out that the daughter was diagnosed with BPD, PTSD, Anxiety, and Depression (admitted publicly in a Facebook post, unbelievably). Even spending a lot of time as part of the family, I never appreciated their struggles until I had a few decades of perspective.
This might seem like I'm agreeing with your mom, but I'm not. As my T said, "everybody has wounds."
I know families where, despite struggles and bumps on the road, are well adjusted. My mother's older sister raised such a family (sans the one adopted kid who went off the rails in adulthood... .I'm adopted, too, so I'm not picking on adoptees, but rather making an observation).
I think you already know the answer to the negative side of your question. For me, even at 12, I knew it wasn't normal for my mom to dumpster dive for produce. Nor was it normal to go from 1983 to 1883 literally overnight, with no electricity, plumbing, heat, but kerosene lanterns. 30 years later, my mom would say, "I did the best I could!" Maybe, but it wasn't normal.
We all survived the physical aspects of our childhoods. Being here, even those lurking yet not posting, is a testament to we being survivors, like it says in the manual to the right of the board. It's the emotional wounds which bind us. To each other in a good way; to the past, maybe not as much. I first landed here due to a romantic relationship ending, and found my way here later, having started to put things together by looking at the past. A few members come from the other direction. Looking into the past and evaluating things may help us not to repeat past relationship dynamics going forward.
It will likely be like extracting blood from a stone to go down the path of getting her to see it from your point of view. As I said, my mom told me what she did, then started to tear up. It was an opposite reaction from that of some parents here, which can be harder to deal with. I let it go. Partly because I felt sorry for her, and partly because I was never going to get validation from the person who hurt me. Radical Acceptance? Maybe.
A very senior member here once said, "no one's coming to rescue us." I think least of all the pwBPD in our lives. That leaves us (and peer group here for support
