Factors that led to their decision
Before the incestuous events with the daughters occurred, the family experienced some awesome and heartbreaking events in a very short period. They had to run from Sodom in order to save themselves. They then saw the aftermath of Sodom and Gomorrah TOTALLY destroyed and wiped completely from the face of the earth. Then, not only is Lot's wife turned into salt, they must flee yet again out of fear and end up living in a cave. Would any of us not feel a bit distressed, uptight, confused, and afraid of what might happen next if we saw and experienced what they did?
It certainly seems the daughters panicked when they were at the cave with their father. This may have led to their confused thinking, which led them to make conclusions that were not accurate, which were then used to justify their impulsive reaction to the situation. The Bible states that they justified having sex with their father because they BELIEVED all men were dead (Genesis 19:31)! This, however, shows the daughters acted impulsively and did not question their assumption that all men were gone. They forgot they left the city of Zoar, which surely had some men in it, AFTER God has completed punishing Sodom and the surrounding cities of the plain for their sins.
29. And when God destroyed (past tense!) the cities of the plain, it came to pass that God remembered Abraham . . . 30. And Lot went up out of Zoar, and lived in the mountain, and his two daughters with him . . . (Genesis 19:29 - 30)
On the surface, the desire of Lot's daughters to continue the human race after Sodom and Gomorrah is certainly noble. Their behavior, however, was based far more on their skewed thinking brought on by fear and panic than anything else. As for the father, he sinned willingly, but not willfully. He succumbed to human nature and put himself in a compromising situation that led him to do that which he normally would not. In the final analysis, based on 2Peter 2:4 - 9, God ultimately forgave him for his errors.