The Duke of Milan is Silvia's ridiculously over protective father. Seriously. He's the kind of guy who locks up his daughter at night so she can't sneak out: "I nightly lodge her in an upper tower,/ The key whereof myself have ever kept;/ And thence she cannot be conveyed away" (3.1.2). Yikes! Sounds like something out of a fairy tale, don't you think? When the Duke catches Valentine with a rope ladder and a steamy love note addressed to his daughter, he puts two and two together and does what any Shakespearean father would do – he flips out and banishes Silvia's boyfriend from his court, on pain of death: "Be gone. I will not hear thy vain excuse,/ but as thou lov'st thy life, make speed from hence" (3.1.18).
To some extent, the Duke is just as dangerous as Proteus in that he stands in the way of the lovers' happiness. His character also seems to anticipate the powerful Prince of Verona in Romeo and Juliet, who uses his clout to banish Romeo. In Two Gentlemen of Verona, the Duke is the guy who doles out all the punishment – this becomes even clearer when we learn that the forest-dwelling outlaws are former noblemen who have also been booted out of the Duke's court. At the same time, the Duke also seems to anticipate some of Shakespeare's other overbearing fathers. Like Juliet's dad, Lord Capulet, he's insistent that his daughter marry the man of his choosing and he threatens to throw his daughter out on the streets when she disobeys. After learning of Silvia's plans to elope, he declares that he's resolved to "turn her out" without a "wedding-dower" because she's so disrespectful and irreverent (3.1.7).
The Duke also tends to speak about his daughter as though she's a piece of property (his property) that can be stolen away from him or bestowed upon another man. Check out this exchange between the Duke and Valentine in the play's final scene:
[…] Sir Valentine,
Thou art a gentleman and well derived;
Take thou thy Silvia, for thou hast deserved her.
I thank your grace; the gift hath made me happy. (5.4.1)
We see this kind of attitude in plays like Taming of the Shrew, where Baptista Minola arranges his daughters' marriages like a businessman, and in the tragedy of Othello, where Brabantio interprets his daughter's elopement with Othello as a kind of "theft" (Othello, 1.1).