What is the essential conflict in Wednesday Wars?

The essential conflict in The Wednesday Wars is one between expectation and experience.
This conflict can be seen throughout the novel. For example, Holling has an ambivalent relationship with his father. Yet, despite his father's obvious failings, Holling continues to hope for the best. Most of the time, however, Mr. Hoodhood disappoints Holling. A prime example of Mr. Hoodhood's disinterest in Holling can be seen in the Mickey Mantle episode.
Accordingly, after playing the part of Ariel in The Tempest, Holling rushes outside, where his father is supposed to be waiting. Mr. Hoodhood had promised to take Holling to Baker's Sporting Emporium to see Mickey Mantle. Despite his disappointment, Holling manages to act quickly. He flags down a bus and begs the driver to take him to the stadium.
For his part, the driver takes pity on Holling. When Holling gets to the stadium, however, more disappointment awaits him. Upon seeing Holling in Ariel's costume, Mickey Mantle refuses to sign an autograph for Holling. Meanwhile, Danny Hupfer returns his own autographed baseball to Mickey Mantle after witnessing the athlete's rude treatment of Holling. Both Danny and Holling learn that sometimes, expectation does not correspond with experience. It is a painful life lesson.
Another example of this conflict is when Mrs. Bigio (bereft of her soldier husband) lashes out at Mai Thi. For her part, Mai Thi has also suffered, but she is too stunned to respond to Mrs. Bigio's pain. For both, the expectations of hope have been crushed. Mai Thi is displaced from her home, while Mrs. Bigio's husband dies at the hands of the Viet Cong in Vietnam. For Mrs. Bigio's husband, there is no victory celebration or triumphant return home. Instead, the warrior intent upon removing the scourge of communism from Vietnam dies in a foreign land.
Meanwhile, for Mai Thi, there is little hope that she will be able to return to her country of origin in the near future. Her hopes for safety and security are dashed upon the altar of war.
So, again, there is the discrepancy between expectation and experience for the characters in the novel.

The main conflict is between Holling and Mrs. Baker. At first, Holling thinks that Mrs. Baker hates his guts. She comes across as quite a stern, forbidding character who always seems to be on his case. But the problem is that Holling doesn't really know Mrs. Baker at all, not the real Mrs. Baker, at any rate. He just sees her as an unbending authority figure.
But when they start reading Shakespeare together, things change. Holling sees a different side to Mrs. Baker and realizes that he's got her all wrong. Gradually, a bond of mutual respect and trust develops, which provides resolution to a conflict based on misunderstanding. In finally learning to accept Mrs. Baker for who and what she is, Holling's also overcome a conflict that most of us have to deal with at some point in our lives: the gap between what we perceive to be the truth and what's actually true.