Atticus and Alexandra disagree about how to deal with the children. How does Atticus handle the situation?

In the novel, there are two major disagreements between
Alexandra and Atticus: raising children and race. 

When it
comes to raising children, Alexandra is much more traditional and conservative
(conforming to the norms in society). In particular, she wants Scout to act like a lady.
As it stands, Scout is very much a tomboy. This is why Alexandra tries to make Scout
wear a dress. She should act like a proper lady and look like one. Atticus does not
concern himself with these things. Instead, he wants Scout and Jem to be children. So,
he does not impose social constraints on them. The very fact that his children call him
Atticus is telling. 

Second, Atticus does not believe in
shielding his children from the ugly racism in the world. To a degree he does, but by
the end of the book, he allows both Jem and Scout not only to know but also experience
the racism in Maycomb. Alexandra would very much like to protect the children. For
example, when Atticus talks about race freely in the house, Alexandra is shocked. She
says:

"Don't
talk like that in front of them... Like that in front of Calpurnia. You said Braxton
Underwood despises Negroes right in front of
her."