Yep. Shakespeare's Queen Eleanor is one of "those moms." She will do just about anything to make sure her son John gets to stay on the English throne—even if it involves hurting her young grandson, Arthur. You did notice how she calls Arthur away for a little chat with "grandam" after he's been taken prisoner (3.3.14), right? Well, she's not interested in giving the kid milk and cookies to make him feel better about being locked up. She does it so King John can tell Hubert to kill the boy.
Yikes. Watch out for Grandma.
So, why is this woman cool with John snuffing out her grandson? Because she knows that Arthur has a better legal right to the throne, that's why. From her private conversations with John, we can see that she has no high-minded ideals about him being the rightful heir to the throne. Actually, she thinks that his legal right is shaky.
When King John brags about his "right" to keep the crown, Eleanor says, "Your strong possession much more than your right" (1.1.40). Translation: Eleanor knows John's legal right is shaky, but she also knows that he's powerful enough to maintain the crown by force.
We will say this: Queen Eleanor is one tough cookie. She encourages John to hang on ferociously to what he's got. When a messenger tells King John about Eleanor's death toward the end of the play, it's clear that John has lost a major part of his support network. This mom is intense, and in a lot of the ways, she's the one running the show in England.
From these details, we can see that traditional gender roles don't apply to Eleanor. In her day, the so-called ideal woman was supposed to be silent and obedient; Eleanor is neither of these things. Still, it's possible that her thinking remains limited by the standards of her time—as in Act II, Scene I, when she and Constance keep accusing each other of being promiscuous.
That said, given the political consequences of inheritance in the world of King John, it's hard to figure out these women's actual attitudes from what they say in public. Could Eleanor and Constance's schoolyard insults just be one more way of getting ahead, using the limited means available to them? We think it's pretty likely.
If you're having any trouble picturing the character of Queen Eleanor, just check out these scenes from the 1968 movie The Lion in Winter, with Katharine Hepburn as Eleanor, Peter O'Toole as Henry II, and a young Anthony Hopkins (in his first film role) as their son, Richard the Lionheart. In these clip, just like in Shakespeare's play, Queen Eleanor comes off as devious, conniving, and totally without remorse as she relentlessly pursues her own goals.
(By the way, this movie isn't based on Shakespeare's King John, but both portray Eleanor's character in a similar way.)