A key moment of conflict could be the conflict between the man and his wife, which results in her committing suicide. Their conflicting views on life and survival in this post-apocalyptic world differs greatly, as obviously do their opinions.
The woman states that she no longer wanted to live as soon as she gave birth to the boy, showing a lack of desire for survival, quite the opposite to the man, who always seems to want to carry on - whether it be on a journey to find a place where there is food, or the journey south.
An alternative moment of conflict could be between the road rat and the man, whose morals and ethics are completely contrasting. The road rat is one of the bad guys, who would kill another human for food in order to survive, whereas, the man and boy consider theirselves the good guys, and they would never eat humans. Their difference in lifestyle, morals and ethics create conflict.
I hope this helps :)
A key moment of conflict in 'The Road' really depends on the meaning of the word. Conflict for the reader or conflict for the characters? Either way, I will use an example for both readings.
A key moment of conflict for the reader is when we are forced to watch the boy move on to another family after his father has passed away. We feel as if this is too good to be true, especially after the many dangers that have progressed throughout the book (e.g. the roadrat, the woman committing suicide etc.), so do we feel happy for the boy, or do we worry about his wellbeing?
In terms of conflict for the characters, a good example is the interaction with the thief, as the boy begs his father to stop, whilst the man is taking revenge for all previous greviances on another human being - effectively killing him. This is important because it shows the genuine personality differences (and hence conflicting emotions) that the two main characters possess