I think I found it

All under 10
Johnson, if I'm tracking with your posts, the kids are her kids, not yours? Is that true?
It is excruciating watching the impact of BPD parenting on kids. My H's kids' mom has many BPD traits, and stepparenting has been really difficult. It's so painful seeing the kids believe the most twisted stuff. Believe me, I know.
One of the (many) difficult things about interacting with a pwBPD is that BPD is a really fundamental pattern of thinking that pervades the closest relationships and can show up as dysfunctional and rigid relational "tropes" or "structures" imposed on what should be normal interactions.
What I mean by that is -- for "broadly normal" people, you might send a book to me saying "hey, I think this will help you", and I can receive it and be like "hmm, I never thought of that before, but I guess I'll check it out", and later I might tell you "well, I thought chapter 2 was interesting, and I might try the stuff in chapter 3, but the rest of the book didn't really apply. Good read though".
There's no drama, ulterior motives, competition, etc in that interaction. It's basically normal.
For pwBPD, many relational interactions happen in the context of their rigid and fundamental thinking patterns, that they are always the Victim, and therefore someone else they're interacting with must be the Villain, and someone must Rescue them or Take Their Side. That's a pretty typical rigid pattern that the BPD wiring imposes on interactions.
So, if you were to send a book to your ex, even anonymously, instead of that info getting through to her, her disordered thinking might impose a rigid, stereotypical framework on what's happening: "Kids, someone sent me this book... I can't believe it, why do they hurt me so much? I'm a great mom, aren't I? Kids, aren't I a good mom? Whoever sent that is the one who needs the book, not me! I don't have any problems! Don't we hate whoever sent the book? Aren't they dumb?"
That would be an example of BPD thinking at work -- taking an innocuous situation and framing it with rigid roles of Victim (your ex), Villain/Persecutor (the book sender), and Rescuers (the kids getting pulled in to prop up Mom's emotions). All without the helpful info in the book making an impact. An example of that rigid, role-based mindset would be the
Karpman Drama Triangle.
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All that to say, because of the rigidity and no-win mentality that can be present with BPD, if we want to have an impact on those close to a pwBPD, it has to be
"sideways" and through us modeling healthy skills like validation, reasonable responses, managed emotions, and mindfulness, for example. The healthier we can become, the more impact we can have on those influenced by BPD. Our
Tools and Skills Workshops are a good place to start.
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What kind of time do you have with the kids these days? Anyone else in their lives that you've stayed close to?