Both my sister and her husband and I have struggled with this issue. My brother in law (I'll call him John) is one of 5 and his mother "adores" one of his other brothers, but the ONLY one who helps her with anything from large to small is "John". The others seem to think that because he lives closest its no big deal. My first husband was the youngest of 3...again, we lived closest so it was assumed we would do whatever Mom needed (again, everything from taking her shopping to home repairs) and the others went about their life. My husband's mother developed Alzheimer's. We brought her into our home and cared for her like a child. Her other children would call on Holidays but made no effort to come see her more than once or twice a year. NO, they didn't live across country....they both lived no more than 45minutes away. When we wanted to take our 4 children on vacation with out MOM, my siblings came and stayed at our home to look after her...her own children coulded take the time to fill in for that brief vacation which we were more than willing to schedule at "their" convenience. SAD. My mother in law died several years ago. Her other children felt guilty (as well they should) and no amount of grief on their part will make up for their neglect. She was a wonderful, caring woman....but the stage was set when they first left home and would not make time to see her and she did not complain. "John" and my sister see the same pattern of behavior. Currently "John's" mother is not doing well....the other kids have been better about coming around but it is clear it is only to try to secure their place in her will to get her money after she dies. My best advice for you......do what you feel is right. I did. I have NO REGRETS regarding the care I gave my ex's mother...when we divorced I got very little of our net worth (far less than 1/2). The court saw no value in my caring for his mother or his children. It showed me that REAL value is in how we deal with the intangible things in life and not the money attached to it. My current husband's mother has recently come to live with us. She also has Alzheimer's. I will care for her because I know it is the RIGHT thing to do. I will expect nothing.
By the way....I worked full time until my mother in law required full time care, and work part time now. It is not easy but I'm sure you have a richness your siblings are lacking in caring for your mother. Stick with it. ...Your self absorbed brother will feel bad after Mom is gone but you will feel loss without regret. Depending upon Mom's needs and income there are ways to look for help for her. She needs to hear and see you, but other issues could be handled by "strangers" if necessary.