The Duchess of York is a lot like one of those mama bears who defend their cubs against any and all threats. As Aumerle's mother and York's wife, she's the only maternal figure in the play. When York turns viciously on his son and decides to go tell the king to kill him for treason, she tries to stop him, encouraging Aumerle to take his dad's boots so he can't go (5.2). She eventually shows up at court to beg for her son's life, which is a pretty gutsy thing to do. King Henry, moved by her pleas, agrees to pardon Aumerle. This is astonishing given that, for the most part, women don't have any political voice in this play.
Aside from this moment, we don't see much of the Duchess of York, but she's a pretty important figure nevertheless. When she opposes her husband and defends her son to the king, she shows us that, for some, family loyalty is much more important than loyalty to the king. (This is a big deal, because it speaks to two of the play's major themes: family and loyalty.) Check out what she says to her husband when he threatens to run to the king and tattle on his son:
Why, York, what wilt thou do?
Wilt thou not hide the trespass of thine own?
Have we more sons? or are we like to have?
Is not my teeming date drunk up with time?
And wilt thou pluck my fair son from mine age,
And rob me of a happy mother's name?
Is he not like thee? is he not thine own? (5.2.13)
In other words, the Duchess wants to know how the heck the Duke of York can betray his own flesh and blood. Come to think of it, this sort of reminds us of the Duchess of Gloucester, who argues that John of Gaunt should be loyal to his dead brother rather than King Richard.