The sibling rivalry is briefly mentioned. When Jem and Dill plan to go to the Radley's house, Scout objects. Jem tells her she doesn't have to go which is as much as a dare.
The social conflict comes when Jem is chased off the porch by Mr. Radley, who actually fired shots. The kids go back to the front of the houses to learn that Mr. Radley has, according to Miss Maudie, "shot at a Negro in his collard patch." Miss Stephanie, the neighborhood gossip, clarifies by saying, "Shot in the air. Scared him pale, though. Says if anybody sees a white nigger around, that’s the one." Note the different language used by Miss Stephanie and Miss Maudie. Clearly, Miss Stephanie has accepted Mr. Radley's assumption that the intruder in his garden was black. This shows Mr. Radley's racist attitude and the willingness of others to accept it; unless, of course, Mr. Radley actually believes he "scared him pale."
The children avoid conflict with the adults when Dill makes up the story that they were playing strip poker, in order to cover for the fact that Jem had lost his pants.