nc born, welcome to the forum. I agree with what has already been posted. There is not much you can do if your mom refuses to see a doctor and continues to drink. At some point, she will have a medical emergency and you will need to call an ambulance. When she lands in the hospital with a liver-related condition, it could be her wake-up call. Or she could continue to drink when she is discharged and further deteriorate until her death. This could take a very long time, or could happen quickly. Meanwhile, you need to take care of yourself and your life. That is really the only thing you have control over.
Most alcoholics are malnourished and that sounds like it is the case with your mom. Since she won't see a doctor, it's impossible to know how many of her symptoms are liver related or alcohol related. She doesn't want to see a doctor because she doesn't want to be told that she has to stop drinking, and about the damage it is doing to her body.
nc born, I can only suggest that you try to find an Al-Anon meeting you can go to (or an Adult Children of Alcoholics meeting, which is an offshoot of Al-Anon and which I found to be really valuable) on a regular basis. Allie, I know you said you couldn't find the time, but you only have to go an hour a week and it's a gift you give yourself--a way to cope better.
Ncborn, never feel selfish for taking time for yourself. You have to, in order to reenergize and be any good to others.
Given your mom's story, no wonder she doesn't want to see a doctor! She probably has very bad memories of all that went wrong. If something happens this time, can you take her to a different ER? Does your niece know to call 911 and then you if something happens?
nc, I'm very sorry that your mom didn't keep her appointment. I had a feeling that she wouldn't, though, because she is still drinking. It really does not sound good for her from what you are describing. Short of going to court and having her court-ordered to treatment, or getting a Medical Power of Attorney so that you have some control over the situation, there's nothing you can do. There will come a point where an ambulance will have to be called. There is also the possibility of her going into a coma, which would at least make it easier to get her to a hospital. I'm very sorry.