What is a disciplinarian? This is a person who administers discipline to others, setting the boundaries and keeping people line. Calipurnia is clearly the person who disciplines the children, and sometimes she disciplines Atticus, as well! There are countless examples in the book of Calipurnia telling the children what they can and cannot do. That is what a disciplinarian does.
Calipurnia acts as a go-between between blacks and whites in the story because, while she is black, she is part of Atticus' household, functioning as a kind of family member. She does not replace the children's mother, but she is a loved and respected adult in the household, respected by Atticus and the children. The family does not treat her differently because of her race, and the relationship represents an ideal of respect between the races. Nevertheless, she is still considered part of the black community in the town, and as such, she is someone who "goes between" black and white people.