In Chapter 9 of To Kill a Mockingbird, after his peremptory spanking of Scout for fighting with Francis and for using bad language, Uncle Jack comes to Scout's room to talk with her.  He, then, provides Scout the opportunity to talk with him and explain her side, as she tells him that Atticus always does.  When Uncle Jack learns what Francis has said about Atticus, he is very upset with the boy.  However, he promises not to mention anything to Atticus as Scout requests.  She tells her uncle that Atticus has told her not to let anything she heard about her father upset her.

Later, as Scout overhears her father and Uncle Jack talk of the forthcoming trial of Tom Robinson, Scout is detected by her father and told to go to bed.  Once there and wondering how he knew she was listening, she also reflects,

Uncle Jack was a prince of a fellow not to let me down.

During their conversation, Uncle Jack has kept his promise and not revealed the context of the altercation betwee Francis and Scout.  This little scene and the conflicts of Chapter 9 are examples of social realism as Harper Lee portrays a family reunion with less than perfect family members.  In addition, the reader learns more about Atticus as he steadily becomes the voic of reason.  As Jack listens to his brother, he realizes that Atticus's strength lies in his calmness.  It is this calmness and integrity in Jack that endears him to Scout, as well.

What you are talking about happens in Chapter 9.

Scout is mad at her Uncle Jack because he spanks her (or something -- it's not stated clearly) after she beats up her cousin Francis.

They manage to become friends again because Uncle Jack does a couple of things.  First, he listens to her side of the story later on (after Scout tells him that it was wrong of him to spank her without hearing her side).  Second, he does not tell Atticus why Scout had beaten Francis up.  Scout does not want Atticus to know she beat some one up for calling Atticus names.