One of the complaints Jem Finch consistently has about his father, Atticus, in To Kill a Mockingbird by Harper Lee is that he is old, or at least old in spirit. Atticus refuses to play in the church football league like the other dads do with their sons, for example. 

Scout is depressed because her dad does not have a cool job like all her friends' dads have; even when Miss Maudie tells her that Atticus can build an airtight will and serves his fellow man humbly and honestly, Scout is not impressed.

Both of his children are disgruntled because Atticus is too much of a fuddy-duddy to let them have rifles like everyone else they know (or so they claim).

Atticus's brother, John Hale Finch, seems to the children to be everything Atticus is not. The kids call him Uncle Jack, and he is the life of the party, much like you might expect a single younger brother to be. He is a doctor, and he is also a lot of fun. He is the one who gives Jem and Scout what Atticus will not. At Christmas one year, he surprises them with high-powered air rifles and teaches them to use them. They are thrilled.

Uncle Jack and Atticus seem to get along just fine, sharing the same views about black people, something which is not shared by their sister Alexandra, as we know. Jem and Uncle Jack seem to get along fine, as well, and Jem obviously respects his uncle because he warns Scout not to cuss in front of him. Otherwise, their relationship as depicted in this novel is minimal.

We do hear more about the relationship between Scout and Uncle Jack, but that makes sense because Scout is the narrator and is telling her story. Their relationship is good in the end, but they do have a rather bumpy incident in chapter nine of the novel. 

When the Finch family meets at Finch's Landing for Christmas, Scout is taunted by her cousin Francis about Atticus and his choice to defend Tom Robinson in court. He repeats some things his grandmother, Aunt Alexandra, has said, including “[he] lets you all run wild” and “now he’s turned into a nigger-lover.” The hot-headed Scout cannot let such taunts go unnoticed, of course, so she socks Francis in the mouth.

Though he gently bandages her hand, Uncle Jack punishes Scout for her behavior before hearing her side of the story, behavior she finds inexcusable for an adult. She scolds her uncle and reminds him Atticus would never have done such a thing.

[You] never stopped to gimme a chance to tell you my side of it — you just lit right into me. [Y]ou told me never to use words like that except in ex-extreme provocation, and Francis provocated me enough to knock his block off." 

Atticus agrees with his daughter, and Uncle Jack is wise enough to give some consideration to Scout's arguments. Even more impressive, at least to the impressionable Scout, is the fact that her uncle was humble enough to admit he was wrong and ask for Scout's forgiveness. 

Because of this, as well as the fact that he keeps his promise not to tell Atticus why she got in a fight with Francis, Scout loves her Uncle Jack even more after this incident than she did before it happened. He, like Miss Maudie and her father, treats children with extraordinary levels of respect.

Both Jem and Scout love and have respect for their uncle.