Not giving medical advice, but would like to ask who diagnosed your mom? And have you had more than one opinion?
Even though she has and is still drinking, there is also a form of Alzheimers that is 'early onset' as in hitting the person in their late 40's to early 50's.
If no second or third opinions have been checked out, it might be a good thing to do, as then you could apply for SSI or SSDI if she worked in her earlier years. And with a diagnosis of Alzheimers you would be able to get her placed in a home that has a section for Alzheimer patients (very secure). And SS would pay for the home.
Just a thought. It might ease a lot of the stress you are feeling at this time.
Please keep posting and let us know how YOU are doing as we do care very much.
Love and hugs,