To purge infected blood, such blood as hers. (2.5.21-26)
Having learned from Bosola that the Duchess has just had a baby, Ferdinand straight-up loses it. The Duchess's blood is his own, and he can't stand the idea of it mixing with that of a social inferior. Gasp! What's especially wacky here is that at this point Ferdinand has no idea who the Duchess has been making babies with. Heck, for all he knows it could be another aristocrat. To Ferdinand, it's as if anybody outside of his direct family has "tainted blood," and that real purity can only be maintained by the Duchess's total chastity.
I could kill her now
In you, or in myself, for I do think
It is some sin in us heaven doth revenge
By her. (2.5.64-66)
Ferdinand, having found out about the Duchess's pregnancies, is venting to the Cardinal. Just as he can't distinguish between the Duchess's blood and his own (see Quote 1), he also can't distinguish between her behavior and his own. To Ferdinand, the Duchess's taking a lover (he doesn't know she's married yet) isn't the independent choice of a free woman, it's an act that has immediate bearing on him. In other words, he thinks her sexual behavior not only affects him, but is also somehow happening because of him. Um, get over yourself, buddy.
Ferdinand: I am to bespeak
A husband for you.
Duchess: For me, sir, Pray, who is't?
Ferdinand: The great Count Malateste.
Duchess: Fie upon him!
A Count? He's a mere stick of sugar candy,
You may quite look through him. When I choose
A husband, I will marry for your honour. (3.1.38-44)
Ferdinand is pretending to offer up a husband for the Duchess, whom the Duchess immediately rejects as flimsy. Notice that, even when she's pretending to cooperate with Ferdinand's plans for her remarriage prospects, she talks about "choosing" a husband—he can line 'em up, but the selection has to be left to her. Also, notice that she says she'll remarry for Ferdinand's "honour"—what do you think she means by this? Is she referring to lineage or merit?
She's an excellent
Feeder of pedigrees […] (3.1.5-6)
Antonio's welcoming Delio back to Malfi and is getting him caught up on the Duchess's baby-making activities. This is her brothers' worst nightmare: the Duchess is, apparently, really good at getting pregnant and birthing healthy children, upon whom she confers her noble "pedigree." The rub, though, is that Antonio's the father, and the pedigree of the brothers is getting passed down to what they'd consider mutts (or "cubs," as Ferdinand later calls them). How rude.
Duchess: You get no lodging here tonight my lord.
Antonio: Indeed I must persuade one.
Duchess: Very good.
I hope in time 'twill grow into a custom
That noblemen shall come with cap and knee
To purchase a night's loding of their wives. (3.2.2-6)
This is that really sweet scene in the Duchess's bedroom where Antonio and the Duchess are teasing each other. This is neat for two main reasons: first, because you simply don't often get these detailed close-ups of domestic relationships in Renaissance plays. Enjoy it while you can.
Second, because it gives us insight into the particular kind of marriage the Duchess and Antonio have: they're joking about how, if a man wants sexual access to his wife (which was, conventionally, a given), he'd better come crawling on his knees and ask real nice. The Duchess seems to have beef with "custom"—she frequently insists that her decision to remarry, for instance, is totally within custom, even citing the church for authority. At other times, she makes it clear that she thinks custom is stupid, and that the world should work a different way.
For know, whether I am doomed to live, or die,
I can do both like a prince. (3.2.68-69).
Like a boss, we think she means. While this may not look like a family quote at first glance, look at the context: Ferdinand has discovered that she's been making her own new family against the wishes of her aristocratic family (him and the Cardinal). At the moment where he's threatening her as her male relative, she asserts her political position. This this is actually kind of reminiscent of the moment when she tells Bosola, right before her death, "I am Duchess of Malfi still" (4.2.132). You go girl.
Thou are undone;
And thou hast ta'en that massy sheet of lead
That hid thy husband's bones, and folded it
About my heart. (3.2.111-14)
Oh, who cares about how happy your marriage makes you, what about moi? Ferdinand's confronting the Duchess, telling her that her unchastity is personally hurting him, which is clearly all that matters (not). These lines are particularly interesting when you look at them next to the Duchess's earlier words to Antonio, "This is flesh and blood, sir, / 'Tis not a figure cut in alabaster / Kneels at my husband's tomb" (1.1.445-47)—go check out Duty Quote #3 for more on this line. By insisting on her status as a living, breathing woman, the onus of the Duke of Malfi's tomb is transferred from her to Ferdinand; the Duke's coffin is "folded around" Ferdinand's heart.
Damn her, that body of hers,
While that my blood ran pure in't, was more worth
Than that which thou wouldst comfort, called a soul. (4.1.117-19)
To Ferdinand, the Duchess isn't really a free, thinking human being so much as she is a vessel for his bloodline. We're not given any indication that he or the Cardinal have children, so the Duchess also becomes the only way of perpetuating (or, you know, tainting) that bloodline. The Duchess's blood is his blood, and to Ferdinand that means that, to control himself, he must control her. Twisted, right?
I have so much obedience in my blood
I wish it in their veins to do them good. (4.2.159-60)
"Obedience" is probably not high on your list of words to describe the Duchess. She speaks these lines as Bosola presents her coffin (courtesy of Ferdinand) to her. The "obedience" the Duchess speaks of probably isn't to her brothers—what do you think it refers to? Also, when she says she says she wishes "it" were in her brothers' veins, do you think she's referring to her obedience or to her blood? What are the implications of those substitutions?
You have bloodily approved the ancient truth
That kindred commonly do worse agree
Than remote strangers. (4.2.260-63)
This is spoken by Bosola, remarking that the Duchess has more friction with her brothers than do people who've never even met. Do you think that this play is family drama, though? If you had to describe this play to a "remote stranger," would you tell him that it's about the "bloody disagreements of kindred"?