She is tired and says AA is putting massive pressure on her blackmailing her if she doesn't do extra meetings they will drop her.
This doesn't sound quite right... Perhaps you misunderstood what she said? Unless she meant her sponsor said they couldn't sponsor her any more, but in that case she could ask someone else to sponsor her. I don't have first-hand experience of AA myself but my understanding is that nobody is asked to leave a particular meeting unless their behaviour is endangering others.
Regarding the living situation - I assume she is in a rental contract? How long is left? Has she tried contacting the landlord directly to ask if she can get out of the contract? I did this when wanting to leave a contract early - I'd signed up for a year but needed to leave 5 months in. They were fine with me moving on as long as they found a new tenant and I paid rent until the new tenant moved in. Of course that would only work if her ex is also willing to move out at the same time, which may be the problem here.
I'd suggest she get in touch with Womens Aid to see if they can offer any other advice, as her relationship was abusive.
Trip to GP might also be in order if she is self-harming.
I would suggest she contacts Shelter for advice on housing. I know there are foster organisations that will take animals temporarily for people in difficult housing situations. Would that be a possibility for her?
Although I can understand she might be heartbroken to be parted from her dog, at this point remaining in a horrible living situation with an abusive man is probably jeopardising her sobriety and is clearly having major negative effects on her mental health.