Death often causes people to reexamine their own life, to prioritize, and to try to live more fully. In that way, it can lead people to give up old grudges, to spend more quality time with loved ones, etc.. Furthermore, grief is a powerful emotion that can either bring people together or drive them apart, depending on how well it is handled. Certainly, death can bring people closer.
As for Pa (Bayard) and Billie Jo, the latter seems likely. The grief caused by the fire is too much for either. Bayard not only placed the bucket of kerosene beside the stove, but he also appropriated the family's savings to finance his drunken night in the pub as his wife was dying. In this respect, Hesse comes close to making Bayard a villain. Although Hesse based the incident of the kerosene accident of a real event documented in an Oklahoma newspaper, from the perspective of fiction, it is inconceivable that a seasoned farmer like Bayard would have brought kerosene into the house, much less left an open bucket near flames, unless he had malevolent intentions. He never explains, or apologizes for this action. But even if readers are willing to believe that leaving an open bucket of kerosene, which has a strong odor and could never be mistaken for water, was an oversight, his blazon abandonment of responsibility to his dying wife was a heinous act that Billie Jo quite rightly cannot understand or forgive.