Firstly, it is really important to remember that by finding reasons for discomfort, we are trying to unravel the hurt and not attempting to place blame on anyone. As parents, we (usually) do what we consider to be our very best and I always look at our intention - if the intention was good, then the consequences, even though not as we expected or wanted, were not intentional and we are not to 'blame'. Of course parents affect the way in which our children live - we wouldn't bother to teach them anything if this wasn't the case. But we are all human and we start with no children, so we are always learning. Your wife is not responsible for your daughter's pain, as she is not responsible for her own.
Yes, I still think EMDR would be worth pursuing. You would perhaps need to run a few details past the individual therapist to ensure they are happy to take your daughter as a client - look for one who has experience with younger people if you can, although it's fine if there isn't one near to you.
The actual underlying issues may not be very obvious, as they will exist in the subconscious mind of your daughter - and they are usually irrational. This is because they are created under highly emotional situations and are often a child's interpretation of the situation - which can be incredibly skewed, and therefore more painful than an adult would imagine. A young child often interprets the world with them as a central figure and they often blame themselves for life events (parents divorce, arguments, the death of the family dog, etc. etc.) - it is even possible that your daughter felt guilty and responsible for Mummy's pain. However, she probably won't consciously know this and if this is true, it is better that it comes out through therapy rather than conscious discussion. Alison's conscious mind would probably say 'don't be daft'.
Substance use is usually a numbing of emotional hurt, so there is some kind of hurt beneath the surface - a relationship of any kind could be another searching for support. I think you may be surprised how much EMDR could help, if your daughter is willing because it frees a person from the past and lets that person live for the future. Mention the Borderline, but it should be OK to go ahead. Best Wishes for a successful outcome, Sarah