Why do you think Antigone and Ismene seem to have so much trouble, at first, agreeing with each other?
Like so many other sisters, Antigone and Ismene seem to have a complicated relationship. They want what's best for themselves and others, though they do not agree.
In the beginning of play, Ismene disagrees with Antigone’s idea that she should go against Creon’s orders and bury their brother regardless of the consequences of death. According to Greek tradition, when a person dies, the women in the person’s immediate family are responsible for carrying out the burial rituals. Without the burial rights, a person’s soul cannot be released from the body to join the other’s who are dead and rest in peace. If the body is dishonored then the soul remains dishonored. Antigone feels that it is the decreed law of Zeus to bury her brother honorably, no matter what he did in life. Antigone believes that Zeus’s law is more important and prudent than Creon’s law forbidding her brother’s burial because of his traitorous attack on Thebes.
Ismene, of course having already lost their father and mother through dishonorable means and now both of her brother’s, fears losing Antigone too through the consequences if Antigone disobeys Creon’s decree. Because Ismene is focusing on the present situation and not analyzing which is more important—Zeus’s law or Creon’s—Ismene is willing to argue with Antigone and put more importance on Creon’s drecree. So, in the beginning of play Ismene argues with Antigone, begging her not to burry their brother because she doesn’t want Antigone to die too.
Later in the play, after Antigone is caught, Ismene claims that she helped Antigone bury Polyneices and begs Antigone to let her share the blame. Again, Ismene does this because she cannot bear to be without her sister and be the only one of their family left.
A major reason why both of the sisters have disagreement with one another is that they seem to be representing different conceptions of women. Ismene is seen as a more traditionalist idea of a woman. She does not seek to voice opposition to the social and political order and represents the idea of adhering to structuralist conceptions of reality. Though she has the same bonds to her brother, Ismene does not outwardly defy Creon's order, suggesting that women must follow the law in order to maintain justice. This is diametrically opposed to Antigone, who believes that justice is something that has to be voiced and pursued at all costs. She does not feel bad about opposing Creon's order, which she sees as the embodiment of injustice and unfairness. In her, the conception of woman offered is one where individuals must speak their mind and argue their point by any means necessary.