ETA: Rereading your post: I guess I missed this the first time -- Your brother was just in rehab, and his wife is posting a picture of him drinking? That is just bizarre. I change my response about apologizing to her, but the rest of my response stands. You don't like the photo. You are happy that your brother is now in rehab. They are just going to have to be mad, if that's how they wish to feel.
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I think you should just send her an FB message (you can do that without being her FB friend), reiterating that sorry you are deleting her, it's not about her but just that you can't tolerate that picture of your brother, and you particularly can't do so because you are a teacher.
Then, when you eventually have to see them, you act civil and polite, as you normally would with anyone. If your brother says anything to you, say "I'm sorry brother, I love you but I just can't tolerate or enable your addiction." Just keep your statement minimal, and then don't engage in argument. If he tries to argue with you, just repeat your statement, and walk away.
And that's all you can say. When my brother was drinking, I had no problem telling him what I thought. He didn't have to like what I said or like me, but I wasn't going to pretend his problem didn't exist, or enable it. His wife took the baby and left for a month and I'm very proud of my brother that he manned up, and quit drinking, cold turkey.