(((snowy)))
I've read your post several times now, and something that seems to keep hitting me is your sister does seem to have some underlying problems - the cutting, the behavior on important dates for YOU (bridal shower, birthday, wedding), etc.
I am not a professional, but could it be possible the drinking is secondary to a psychological condition? Has your sister been in therapy outside of alcohol treatment?
I'm sorry you are having to deal with this, and I agree with the others that you should involve your family and not carry the load yourself. Your sister has reached out for help and I'm not always convinced that the let go and let them sink applies in every case.
Please keep posting and take care of you first and foremost.