Hi. Welcome to the forum. I am sorry to hear your brother is so ill. His constant detox sounds really awful. As a former alcoholic I can't imagine doing that. What is the point?
Unfortunately there is no way to know how long this could go on. He could continue this way for decades or have a stroke or heart attack and die the next time he tries. 18 years is a long time to dedicate to helping someone who could help himself. He can you know. As a matter of fact if he is to quit for good he needs to do it himself for himself. No one has ever loved someone to sobriety. It has to come from somewhere deep inside the alcoholic themselves. He has to decide that the pain of continuing is worse than any possible pain that could come from quitting. Then and only then can he actually find sobriety and recovery.
You and your mom really need to take care of yourselves both physically and emotionally. Your mother especially could wind up becoming quite ill from the constant stress.
Please find an Al-Anon group near you. The support is amazing