What's the goal here: do the right thing and have self-respect or create the image of success with a "successful" marriage where you are treated like crap?
You need to look inward and see what the answer is. Even the words you use sound like scratching a chalkboard to me, "obey your wife." A wife obeys her husband. A man loves and cherishes his wife when she does that. Things might be too far gone to be salvaged; you might appear to her like a rebellious inmate rather than a man acting normally after all of the indicators of weakness you've given over the years. That really doesn't matter though. You can't control her or other people. You can only control yourself and your own reactions to situations.
If your brother is an addict or something and you're enabling him that's another story. Women sometimes have very good common sense about these things. But if you're just helping him and that's cutting into the salon budget, I would just be assertive, direct, manly, and clear. Tell her, "Look, I'm doing this. It's the right thing. Family's important to me, and I believe that those to whom much is given, much is expected, especially when others fall on hard times. I realize you want me not to do this. And I realize that's why you're hiding out on the other side of the house. But this is not going to change. I'm going to do this. And not only that, I expect you to remain my wife and love me and respect me throughout this process. If you can't handle that, then we need to consider alternatives. For too long I've accommodated your whims, even when I knew it was wrong and felt bad about it. I'm not going to do that anymore. It's important to me, my happiness, and my sense of self respect to do this. I will not always do what you want. More important, I will not be controlled by you. You need to understand this. I'm not going to back down on this. If you keep ignoring me and not supporting me in my life and my decisions, I think this marriage is already over. You should figure out what you want to do one way or the other and tell me what you decide. But I'm not playing games here, and I'm not going to tolerate this disrespectful passive aggressive behavior much longer."
You'll feel 1,000,000 times better if you do this. Even if you get divorced, you'll be standing on your feet and feeling the pain of loss and separation as a man rather than grovelling and begging for scraps from your wife, who, if anyone, should be obeying you.