Brian's mother and father have divorced and Brian is flying up to the oil fields to visit his father. Clearly there are custody arrangements that allow for him to visit there occasionally while the majority of time is spent with his mother. 

While there is little to know about how Brian feels about his father, he is consistently troubled by "the secret" that he knows about his mother having an affair. He happened to see his mother kissing another man in a car before the actual story in the book starts. He is thinking about what happened and what he saw when he gets on the plane and comes back to think about it repeatedly during the story.

It is also clear that his mother is not aware of the fact that Brian knows about what she did as Brian clearly feels very uncomfortable telling his mother about it. The lack of trust and unease that Brian feels is clearly an issue between him and his mother.