Who's most vulnerable?
Of the sons and Alais, who would you say is the most emotionally vulnerable?
Alais seems the most probable choice, given her winsome personality. Her remark to Eleanor: "There's no sport in hurting me. It's too easy."
But each of the brothers divulges considerable vulnerability at certain moments. Most striking to me is Geoffrey: "I never remember anything from you and father warmer than indifference. Why is that?" "That was not an easy for question for me, and I don't believe I deserve an easy answer." That reveals a lot of pain behind all his scheming and bitterness and makes me feel sorry for him when I don't otherwise.
John, when he's sitting by the pigs after Henry says Richard will be king. Besides feeling sorry for himself, he tells Richard that Richard was the older brother that John dreamed of. Even Eleanor feels a pang of sympathy for him and cries out, "Oh, Johnny!"
Richard seems pretty vulnerable multiple times: in a few interactions with Eleanor, in his anguish that Phillip's love for him was false and a ruse to exploit him later, in his following sparring with Henry that Richard had always wanted Henry's love but never received it; it always went to young Henry.
The end of the cellar scene, with Eleanor weeping that she had lost Henry, the only person she'd ever loved, and could never get him back, and "Christ, Henry, you don't know what nothing is." Then, "I want to die, I want to die,..." Henry, meanwhile, is beaten and feels he has "nothing." I'd say that's a pretty vulnerable moment, but it doesn't quite count: they are so thick-skinned the rest of the time, and so lost in their vicious scheming and manipulations, that any vulnerability for them isn't the essence of what they are. For the others, it seems to me that vulnerability was at their very core.
I'm sure this qualifies as a "tl;dnr", but this isn't twitter.