I do not want to say that there is only one antagonist in The Wednesday Wars. There are several characters that function in that capacity. Considering the book's title and how Holling initially feels about Mrs. Baker and his Wednesday afternoons there, the reader first assumes that Mrs. Baker is going to be the antagonist of the story. But already by halfway through the novel, it is clear that Holling and Mrs. Baker are establishing a very good and healthy student/teacher relationship. In fact, she becomes almost as much of a protagonist as Holling is.
I would say that there are two main antagonists that remain antagonistic to Holling through the entire story. Doug Swieteck's brother is one. He's a school bully through and through and does everything within his power to make Holling's life miserable. In fact, he goes way out of his way to do it, too. The time he invested doing the newspaper plot goes way beyond normal school bullying.
While Doug Swieteck's brother is unfortunate, he's not an unexpected antagonist. It's school; there are bullies. The unexpected antagonist is Holling's father. The guy is a self absorbed narcissist. That's bad enough, but the fact that he is a father just makes it worse. He doesn't care what his kids want or need. He's into himself, his firm, and his own reputation. He doesn't even bother going to Holling's school functions to show his support for Holling. It's not easy for Holling or his sister to have to live with that type of father. In fact, he's one of the main reasons why Holling's sister ran away. And the guy couldn't even bring himself to help her get back home.
There is one primary and one secondary antagonist in The Wednesday Wars by Gary Schmidt. The primary antagonist in the novel is Mr. Hoodhood. He is driven by nothing but money and prestige and has no real relationship with either of his children. Hoodhood cares more for his architecture firm's reputation and for his own public recognition than he does about his own children. He assumes Holling will take over the company one day (disregarding Holling's own wishes or interests) and forces his daughter, Heather, to work at the firm. He does not attend any of Holling's special events or performances, preferring instead to do whatever best suits him. He refuses to pick Heather up from the bus station once she ran away from home and then returns, and he does not care at all about anything that matters to Holling. Mr. Hoodhood is a selfish and self-absorbed man, qualities which also make him a perfect antagonist.
We never even learn the secondary antagonist's name, but he gives Holling Hoodhood, the protagonist, no end of trouble in this story. He is known only as Doug Swieteck's brother. Holling refers to the bully when he says:
I think something must happen to you when you get into eight grade. Like the Doug Swieteck's Brother Gene switches on and you become a jerk.
Doug Swieteck's brother is always tormenting Holling, who is in Doug Swieteck's class at school. He "invites" Holling to play soccer at recess and then deliberately tries to mow him down or something worse--which we never learn for sure because Holling trips him and causes the bullying boy to get his head checked. Later, he and his friends throw yellow snowballs (none of us, including Holling, wants to know why they are yellow) at Holling. It is true that Holling gets some revenge for that, but he also pays for the act later as Doug Swieteck's brother apparently neither forgives or forgets.
He is always doing little things to get Holling in trouble or just because he likes to humiliate the younger boy. The worst incident, of course, is when Doug Swieteck's brother sees Holling's picture, dressed as Ariel, on the front page of the newspaper and hatches a nefarious plot. First he steals the front page from every newspaper he can find on the porches in his neighborhood; then he spends hours intensifying the yellow of the costume by adding paint to the yellow costume on every page.
None of this would matter except Doug Swieteck's brother then plasters all of these colorized and enhanced pictures all over the school building, including the girls' bathroom and the ceilings. For days, people take them down and more of them mysteriously appear.
In short, Doug Swieteck's brother is a bully who antagonizes Holling both physically and emotionally. A case could be made that the entire eighth grade is an antagonist to Holling, but this one boy is certainly the epitome of a peer antagonist in this novel.