she does have a diagnosis - she self harms and that in itself is a particular type of mental health presentation that requires immediate and considerable input from the cams team. it has a very specific approach to treatment and management - and she is also using alcohol (potentially drugs as well?). the family should be pushing for as much support as they need - tell them not to be afraid of saying they are scared for her or are unable to cope with a situation).
as she is under 18, the professionals may be reluctant at this stage to 'stick' a particular mental health label on her....but given time, assessment, treatment and therapy (she should be getting all three right now and services should be making assertive attempts to work with her even if she is reluctant to see them) it may be that an underlying condition is the root cause of the self harm (possibly depression or borderline personality disorder - the most common cause of persistent self harm in adolescent female teenagers). it may take time to establish a certain disorder and it can also change as time progresses. i have had three different diagnoses over the last 15 years before they have finally settled on my current one (and which i agree with!).
social services will be involved (as she is under 18 and vulnerable given her current social contacts and behaviour) to assess her home and living situation and the capability of parents to support her with her current needs. the mental health team also should have a clear risk assessment and management plan that has been discussed with everybody involved. this should cover what to do when she self harms (wound management, how to talk to her at the time and further contact details for help, for example).
the family should also be supported in knowing when hospital treatment is required for wounds or to take control in a crisis situation where she is at considerable risk of parasuicide (accidental severe injury, disability or suicide). cutting is a risky method of deliberate self harm and sometimes people expect to be found after doing so or completely try to hide what they have been up to and this can have devastating results if things go very wrong - sorry, but your family members should be aware of this.
i'm sorry if this is a bit of a rambling post....but i am a psych nurse, with mental health problems of my own...so have seen and treated lots of people in this situation (and not passing judgement in any way - just trying to help). she is clearly in need of support (as are her parents, i expect) and both mental health and social services should be working together with the family to support this girl in dealing with such a complex and delicate presentation.
if i can help in any other way, i would be glad to do so and will subscribe to this thread to keep an eye out. i hope i haven't spoken out of turn or offended you in any way...but your relatives can work through this successfully if things are dealt with quickly, appropriately and all the young lasses needs are met. sometimes this doesn't happen between different services and you really need to push for things to happen and be as successful as possible. i wish you and you relatives well x