Scout and Dill do indeed hear Calpurnia move from the standard (Southern) dialect that they're used to hearing her speak to a more strongly marked black dialect when they accompany her to church in Harper Lee's novel To Kill a Mockingbird. They also see her stand up to one black woman (Lulu, who's pretty much the black version of the Ewells, despised by the main characters and by most readers) who doesn't approve of white children coming to their black church. Not everything in Calpurnia's behavior is above reproach, however. She addresses Lulu with a coarse term (in a context that's hardly neutral): "Stop right there, nigger."
The most important thing that Dill and Scout learn through their visit to her church, I believe, is that Calpurnia has a full life outside of their house. They've grown up believing that they're all she has, but in reality she has a church, a house, and probably even a family of her own (although, as I recall, the reader never gets to know anything about that family).
In the book "To Kill a Mockingbird" Calpurnia takes Jem and Scout to church in her neighborhood. Once they are around the people of her own color Calpurnia begins to speak in a different pattern and uses different expressions. Scout is puzzled by the change in the way in which Calpurnia talks. She questions her about this. Calpurnia explains to Scout that there is a way she talks on her job in the white community and a way she talks and acts in her own setting. She tries to help Scout understand that the way she presents herself among the people of her community would not be understood nor appreciated or appropriate neither in the white community nor as an employee. Calpurnia also shares with Scout that she has the responsibility of helping Atticus’ children to grow and develop, and it would not be appropriate for Scout to communicate in the same manner as she does when she is home. Scout will need to be able to communicate like white people because she is a part of the white world. In addition, if Calpurnia spoke to her friends and family like she does the white people they would be uncomfortable and feel looked down upon.