Well, my kids were much older when I stopped talking to their grandmother. They were 8 and 11 (turned 12 that week) when the breakthrough crisis started. And we're not totally NC because we still attend family parties, so they see her at those a few times a year.
I just didn't say anything at first. About 6 months went by before one of them commented that we didn't see Grandma S much anymore. So I told them that I didn't like Grandma S's behavior and had decided not to hang out with her a lot anymore because of that.
One of the things my mother did was overshare so I'm careful not to do that with my kids. I brought up examples of things they had been part of, times she had yelled at them or stormed out of the house because of something they had said. I didn't share any private examples of tell them about my childhood or anything like that.
We talked and both of them surprised me by agreeing with me about Grandma S's behavior and even bringing up examples that I hadn't known about at the time.
I didn't say anything about BPD because even though I'm sure she has it, it's just my armchair diagnosis, and also it doesn't matter. What matters is how she treats us. What I said was that Grandma had anger issues and can't control herself and I don't want to be around someone like that. I told them that she doesn't think she has a problem and doesn't think she needs help so I had decided it was for the best to just not hang out with her a lot. I was really careful with my words and kept it vague but clear that we don't allow people to hurt us even if they "can't help it" or it's "just the way they are". Good advice for life in my opinion.
So it's been 2 1/2 years now. They see her at Christmas and family birthday parties. My daughter (now 14) sometimes talks with her but my son (now 10) doesn't. It's not that he's ignoring her, it's that she's become just another adult to make small talk with and he doesn't like small talk

(my daughter however is chatty and will talk with anyone).
I hope that helps!