Hello there and thanks for makjing this clear for me. To my experience people who cut do that to release very strong emotions that they don't feel they can handle. It sounds like your daughter has very powerful emotions and she does not know how to take control of them. I think leaving and going to her friend's place was a way for her to take control of her emotions. It looks like she is very stressed out and felt blamed due to the accident. I don't think she is going to cut herself. I think leaving was a way for her to be safe/ When we talk about being safe in therapy terms we usually mean in her case is she safe from wanting to cut. Those are terms that she learned in order to help herself from cutting. I think she will be better tomorrow. I think the argument with your wife is not about what happened now but about something that bothers her in general. Cutting can be a symptom of another disorder that includes having strong fears about being abandoned. This personality is usally very intense and does not do well in relationships.
BPD patients may also be uncertain about their identity or self-image. They tend to see things in terms of extremes, either all good or all bad. They also typically view themselves as victims of circumstance and take little responsibility for themselves or their problems.
Other symptoms include:
I am glad your daughter is working with a therapist. I don't think your wife did anything wrong. BPD tried to start fights when they feel insecure so the best your can do is to not take it personally and stay emotionally detachedm do not feed into the emotions.
Stay calm and say that you will talk to her later.