The main conflict in the play is between Antony and his conscience. Antony, although a great warrior, is emotionally weak and is driven by jealousy. He desperately loves Cleopatra but also is afraid of her power over him. He is convinced that she has betrayed him to his enemies, yet he is easily duped by her into thinking that she needs his protection.
While it is easy to see Cleopatra as a schemer, the real source of conflict is Antony's indecisiveness. He is haunted by regret—first over abandoning his wife and family for Cleopatra, then for his defeat at the hands of the Romans after Cleopatra betrays him. He is consumed with self-pity. This makes him an easy target, and he is manipulated not only by Cleopatra but by Alexas, Cleopatra's servant, and blind to those who are faithful to him.
In this sense, the conflict of the play is internal. Dryden chooses to focus on Antony's crisis of conscience rather than on the geopolitical significance of his abandoning Rome for Cleopatra's charms. This comes to a head when Antony meets his wife, Octavia, and his children and is overcome with remorse. Even though he says he will return to his wife, Antony is still possessive of Cleopatra and unable to curb his jealousy when he learns that she is interested in another man. Whatever his sense of duty may be, Antony remains a prisoner of his passion for Cleopatra.