Hello and welcome, Preacher!
Your situation sounds frustrating and bewildering -- and, unfortunately, familiar to many of us here. My husband frequently complains about my family's treatment of him and reactions to him, yet, when we're all together, he just sits and glares and looks like he'd just as soon punch someone in the mouth as speak. Does he get that? Sometimes he does. Sometimes he doesn't.
When talking to her when she’s upset, she seems to have no grip on rationality.
Yep. As you've found, talking to her when she's upset is unlikely to net any positive outcome. She's in full emotional mode. Kind of like how they tell you not to try to reason with a small child mid-tantrum. They won't/can't hear you. People with BPD have great difficulty in managing and processing emotions -- and they feel emotions very strongly, perhaps even more strongly than the rest of us.
Anyway, we have a lot of experience and skills we can share with you that can help you. They've helped me. Just curious, have you done much research or reading on BPD? Often, knowing and understanding the disorder can really help us know how to respond to situations in an effective matter. And, as I've learned, often our responses play a large role in how things progress. Not that it's our fault. Not at all. But we do have a part to play.
I hope you don't mind if I ask a couple of questions.
When you give her space and go for a walk, how does that usually go? What do you say or do before you leave?
Do you point out her attitude to her after you've been in social situations? If so, how?
Keep posting and, again, welcome!