How can a young man and his fiancée reconcile their desire to expedite the marriage to avoid sin, with the mother's insistence on delaying it for two years, knowing that the young man fears he may have disobeyed his mother by angering her due to this disagreement?

Your mother does not have the right to prevent you from marrying if you fear temptation (fitnah), nor to ask you to delay it. You should hasten to marry as long as you fear temptation for yourself, while engaging with her gently and kindly, and explaining that hastening to marry is in accordance with Islamic law, citing the Prophet's (peace and blessings be upon him) hadith (definition): "O young people, whoever among you can afford to marry, let him do so." If she insists on her stance, there is no sin upon you if you do what the Sharia (definition) has encouraged you to do.