What should a dutiful son do, who has supported his family since childhood, when his mother asks him to help his younger, lazy brother get married instead of performing Umrah, and he fears being disobedient if he refuses, yet unjust to his wife and children if he agrees?

You are not obligated to pay money for your brother to get married as long as he is able to earn a living, and you would not be disobedient to your mother by refusing to do so. However, if you are able to help him without unduly diminishing your wealth, this is better and brings greater reward, especially if it benefits him and you avoid your mother's anger. Indeed, Imam Malik was asked about a mother who sought something for her daughter, and he was of the view that she should not be provoked.