In Poisonwood Bible do we learn from his wife and daughters enough information to formulate an adequate explanation for his beliefs and behavior?
Yes, we do. Orleanna, his wife, gives us a picture from the early years of their dating and marriage of why Nathan behaves the way he does. His dark, evil side seems to come from his experiences in the Philippines as a soldier in the infantry during WW II. He's hit with a shell fragment and learns later that the rest of the men in his unit were killed during his absence. He feels ashamed and cowardly that they all died and he lived. Orleanna says he cannot "leave the jungle twice". He feels he's showing how brave he is by staying and doing God's will. His guilt eats away at him, and he thinks God judged him as a coward because he didn't die with his unit.
This affects him later in Africa because he refuses to leave with his family although they're in great danger. To prove himself worthy, he thinks he has to save more souls in Africa than the number of men who died. He "felt it had been a mistake to bend his will, in any way, to Africa," and he grew even more hardened in his years there. He's maniacal in his efforts to save himself and the villagers. He can't see the dangers to him and his family and refuses to let them leave. Even after his wife and daughters leave, Nathan stays and reportedly goes mad. He's burned alive because in an attempt to baptize children, he leaves them drowned in the river.