How does Dido and Aeneas duty conflict with their love for each other?
Love and duty are at odds, especially in Book IV, and this is shown in the love Dido feels for Aeneas and the responsibility Aeneas feels for resuming his duties.
Dido's love is a violent force because her emotions have destroyed her self-control. It is like an "inward fire eating her away", and she abandons her duties to her people because of it. She no longer cares about building Carthage, and her people hate her selfish actions. At the end of Book IV, she kills herself, and Virgil, comparing her suicide to a city that has been overrun by its enemies, describes her death "As though ... flames billowed on the roofs of men and gods". Her love for Aeneas has brought only death, hatred, and destruction. She allows her emotions as a woman to replace her duties as a leader.
Aeneas views his love of Dido as a temporary distraction from his real duties and responsibilities. Mercury reminds him of his destiny, and Aeneas, even though conflicted, leaves Dido. He "struggle[s] with desire to calm and comfort [Dido] in all her pain", but love can never supersede his duties. Aeneas returns to his civic responsibilities, leading the people of Carthage to his new city.