How does Holling interact with Doug Swieteck's brother in The Wednesday Wars?

Throughout The Wednesday Wars, though Doug Swieteck's brother is described as a juvenile delinquent bully, Holling emerges triumphantly in all of his interactions with Doug's brother.

The first time Holling emerges triumphantly is when he has to face Doug Swieteck's brother in a soccer game at recess in the opening chapter of the book. The brother is playing forward against Holling, who must play defense. When he sees Doug Swieteck's brother charging him with the ball, Holling first tries to stand his ground, but then flees. He says he leaves his "right foot behind," though. Doug's brother trips over Holling's foot and flies like a missile through the air, crashing into the metal frame of the goal post. Everyone congratulates Holling for taking out Doug Swieteck's brother, even though Holling didn't trip him on purpose.

Another time Holling emerges triumphantly is when Doug Swieteck's brother tries to humiliate Holling by plastering the town's schools with the picture from the front page of the newspaper depicting Holling playing Ariel in The Tempest, dressed in his costume of bright yellow tights decorated with feathers on the backside. Within the same couple of days that the brother goes around taping the picture up all over the town's schools, Holling is also photographed being injured while rescuing his sister from a bus sliding out of control on the icy road. This picture is also featured on the front page of the newspaper, and Holling arrives at school the next day to find someone replaced all his humiliating pictures with his new heroic picture, making Holling triumphant over Doug Swieteck's brother once again.

In The Wednesday Wars, what does Holling do to Doug's brother at the end of January?

We need to remember that Doug's brother was the one who literally littered the school with pictures of Holling in his Ariel outfit dressed as a fairy. Therfore we know that Holling definitely would like a chance to get back at Doug's brother. He gets the perfect chance in January when it is very snowy and, one morning before school, he Holling sees Doug's brother and realises that he has the perfect chance to throw a snowball at him and then run off into school so that Doug's brother doesn't realise who threw it. Note how Holling imagines the scene:

In my mind I could see it all: I pull back my arm, plant my left foot, Doug Swieteck's brother comes sliding into sight, i release the fastball, his face turns toward me at the last moment, and the snow-ice-slush-spitball splatters against his nose. Perfect.

Even though Holling believes it is not going to happen like this, he still goes for it, and it satisfied when it all works out completely as he anticipated. Holling gets his revenge, and as he is studying Macbeth at the time, there is definite symmetry between his life and this play.

What is the relationship between Holling and his sister in The Wednesday Wars?

Holling's relationship with his sister, Heather, is dynamic; it changes by the end of the story. When readers are first introduced to Heather, it is clear that there is quite a bit of antagonism between her and Holling. For example, the first time that Holling speaks to his sister, she tells him that she hates his guts:

"Mrs. Baker hates my guts," I told her. 

"So do I," she said.

"I could use some help with this." 

"Ask Mom." 

It is clear from this exchange that Heather and Holling are not best friends with each other. They really are not even on general speaking terms with each other. That does not mean they do not love each other though. In fact, Holling risks his life to save Heather from a skidding bus. His love for his sister continues to show throughout the rest of the story. It is Holling that pays for her to return home after she runs away and gets stuck. She knows better than to talk to her dad or mom about it, but she knows that Holling loves her and she loves him. When she finally returns home, she breaks her icy shell and hugs Holling. It is her way of saying "thank you" and "sorry" at the same time.

They did not start up again until my sister got off the bus, and she ran out of the diesel combustion and right to me, and we held each other, and we were not empty at all.  

"Holling," she said, "I was so afraid I wouldn't find you." 

"I was standing right here, Heather," I said.  "I'll always be standing right here."