If he has a problem with his common law wife, he needs to file for divorce. Common law marriage is simply a way of getting married. If a common law marriage has actually been established (you can read my guide on the topic for more information) then your brother is legally married and he cannot just toss his wife out of the marital home. He needs to file for divorce and sort out possession of the residence in court.
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Your brother may choose to file for a divorce, and ask the Court to make orders regarding who has use of the residence. This is not a fast process. If your brother believes she is a danger to herself, due to her drinking, he may contact the police, and if they feel she is a danger to herself they may place her on a 72 hour mental health hold. She will be taken to a local hospital where they will sober her up, and then a determination will be made as to whether or not she needs to be held for the entire 72 hours.
Your brother may want to speak to someone to determine whether he is truly married, as not being married may open other options to him.
This legal information is provided for general legal purposes and does not establish a client-attorney relationship. Because of the limited information provided in the question, it is difficult to be certain that Counsel is answering the question correctly. You are encouraged to seek further information from an attorney directly so that follow up questions may be asked if necessary.