This is correct - if you have made a referral to adult social care for housing then it won't go anywhere, the only housing provided by social services is residential/supported living type accommodation.
But, as a social worker in an adults safeguarding team I work with people in your situation very regularly, usually after referrals from the police or from the ambulance service. If you are in England or Wales and see yourself as a carer for her (and it sounds to me like you are) then the local authority has a duty to make s.42 safeguarding enquiries for you of they have reason to believe you are being abused as a result of your caring role
They can support you to liase with other services like Mental Health, Housing, police etc to support you to be safer.
Police I'm afraid are key in this - yes she will get 'a record' but it can also be the catalyst for other agencies to be involved.
In a very similar situation to the one you describe that I was involved in recently the Safeguarding multi-disciplinary team worked together on a range of different actions - police put a Domestic Violence prevention order in place that meant there could be no contact for 28 days which broke the cycle and gave everyone breathing space to consider options. The 'child' in their late teens/early 20s was provided by housing with a supported tenancy with strict conditions around behaviour, adult social care provided support for them to manage their home and to access mental health services. The local domestic violence prevention services offered courses/counselling around their abusive behaviour.
The parent was offered support through domestic violence services, adult social care safeguarding team and victim support and with the back up and support from professionals was able to accept that in trying to keep their child 'safe' they were putting themselves at significant risk of harm.
I am in no doubt that had we not been involved that the parent in that situation would have been seriously harmed at some point by their adult child.