Sorry I read the unchecked BPD (and have zoomed in), and how that's your reason for her poor judgement of people. While yes BPD is hard to manage and get help for to judge that because she is close to someone with it who is struggling means her judgment is bad kinda rubbed me the whole wrong way (but that might be MY BPD). I just know the struggle having been at one point known as on the "lower functioning" side of the spectrum. The stigma attached to BPD is so vast that I only am open and honest about my own issues online since speaking out in RL about it usually leads to people prejudging me. However I do not know your situation but I just wanted to chime in with my two cents about how I hope this person has shown you they cannot be trusted around your LO before you throw in they have BPD and that's why.

Sorry for the little rant, I'm in NO way trying to detract from your issue here with your MIL. She might have other people or behaviors that make you feel uneasy and the BPD friend is just another on the list.