Women are typically vulnerable in Richard II, possessing little power of their own. The Duchess of Gloucester wants her husband's death avenged, but she must depend on the willingness of male relatives such as John of Gaunt for that to occur, and it never does. She dies frustrated. Even someone as high-ranking as Queen Isabel is ultimately dependent upon men for her survival, and at the end of the play, the best she can do is leave England in exile while the man she loves suffers so he will not have to bear the additional burden of having her share his unhappy fate. The Duchess of York illustrates this lack of power in particular: despite being a woman of noble birth, she must beg King Henry to spare her son after he betrays the crown.
While the men in the play are obsessed with questions of power and loyalty, the female characters are more concerned with family loyalty. For the Duchess of York, it hardly matters that her son has betrayed the new king in a "dark conspiracy": he is her son and her love for him overrides any concern for the safety of the crown. When her husband announces that he will allow their son to be arrested, since he believes they must stay loyal to the crown no matter who wears it (it is ambiguous if he believes this or if he is interested in maintaining royal favor), the Duchess claims that if the Duke had "groaned" for their son in childbirth then he would understand how she feels.
The queen prizes love above political power but cannot succeed in saving her loved one as the Duchess could. When she begs the Earl of Northumberland to let the king live in exile with her in Act 5, Scene 1, the Earl says, "That were some love, but little policy," suggesting that love and politics cannot coexist.
In this way, the women become foils for all the power-hungry male characters. Perhaps because love and family are all they have, they do not necessarily care who is king or who is the most loyal to the crown but that their families are kept safe and intact. This is an alternative worldview to the political grasping which dominates the play, one that proves unsuccessful for everyone but the Duchess.