She's undiagnosed and I have read numerous reports that it is probably not best to tell a person they have BPD. I have debated this and concluded that she would not take it well. It would result in a massive downward spiral and self harm I imagine.
However, should I speak to my children about it? I would like them to understand why things are like they are and why mum does what she does, but at the same time I don't want to hurt them or their relationship with her. Would they treat her differently knowing about BPD? I trust myself not to blurt out about BPD in the heat of the moment, but would they be able to do the same?
This is a tricky situation, and I think you raise the right questions/reservations, especially where kids are involved.
I don't have an answer, but there is good information (for reference) here:
PERSPECTIVES: Telling someone that you think they have BPD