If you can change it then it isn't something you can't change. I kinda get the point she's trying to make but the quote she's attempting to use literally already has the concept built in. "God grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference." So she is using her courage to change the things she can but ignoring the other part.
According to her sign. The things she can't change are the things she can't accept, which are exactly the things her sign says she's going to change. Ergo she's trying to change the things she can't change.
doesn't make any sense?