Hi, ZoyaB, and

Thanks for your post. It can feel confusing trying to navigate a relationship with a family member who has BPD. I can tell it's frustrating for you that your SIL won't work with you to find a time to sit down and talk about how to resolve the incident that's troubling you. That's understandable. Healthy adults will try to work through their problems together and come to an agreement about how to move forward. It sounds like your SIL might not know how to resolve conflict that way. Perhaps it is frightening to her to think about the issue or she has learned to ignore problems until others pretend they are gone.
Making an appointment to discuss important issues seems reasonable to me, as it gives the item a sense of priority. It also can be a matter of personal preference. If your SIL doesn't want to do that, that's ok. Your plan to call this weekend makes sense, since you both agreed that would be a good general time. It also makes sense to take care of your boundaries by ending the call when someone speaks disrespectfully to you. You can't control her preferences or actions; you can decide to do your best to live according to your values.
BOUNDARIES: Upholding our values and independence helped me to see boundaries in a way I hadn't before. Maybe there will be something there that will help you, too.
What I hear you worried about is whether she will ever be able to discuss the incident with you enough that you feel it is resolved. If she has BPD, then most likely not, but maybe. One tool that has improved my communication is S.E.T. (Support, Empathy, Truth). There are others, such as DEARMAN, which can be useful when asking for something specific. You can read about some of them here:
Communication tools (SET, PUVAS, DEARMAN). It sounds like this incident must have been a pretty big deal if it means you might not invite her to your wedding as a result. Do you feel like elaborating about it?
Like Turkish, I'm curious what kind of behaviors have been a problem in the past. We'll look forward to hearing from you when you're ready.