Calvinist religious beliefs include a strong belief in the will of God. Sarah is deeply religious herself and believes Providence is God's way of guiding Christians to do the will of God. She feels a Christian must be alert to God's signs that tell a person what God expects of her and be ready to do His will. We already know that Sarah is an intelligent woman because of the way she presents her arguments for a new house to her husband.
Keeping this in mind, Sarah figures that Providence encourages her to move into the new barn. The letter that Adoniram receives, causing him to have to leave is a "sign" to Sarah that God wants her to take this opportunity to make the new barn her new home. In her mind, she would not be a good Christian if she ignored this "sign" of Providence telling her God's will. Even when dealing with Minister Hersey, Sarah again shows her intelligence. He is God's representative on earth, but he is also a man. He's unable to understand Sarah's spirituality because his concern is how Adoniram is going to deal with his wife when he gets home and discovers what she's done. Sarah believes that what happens in their home is between her, God, and her husband and that her decision to move into the barn was partly reached as a result of her prayers to God.
Considering all of this, I believe the author is criticizing the strict gender roles in marriage. I base this on the fact that Sarah outwits her husband, using his own religious beliefs to support her decision to take over the new barn. When the news of what Sarah has done gets around, the townspeople think she is insane or that what she's done has to be against the law because she has dared to defy her husband. Notice she never loses her temper or stops doing her wifely duties, even defending her husband to her daughter. When Adoniram decides to build the new barn instead of a new house, this is the "straw that breaks the camel's back". Sarah then methodically plans how she will get her new house after forty years.