Quote 1
KATHERINE
Young budding virgin, fair and fresh and sweet,
Whither away, or where is thy abode?
Happy the parents of so fair a child!
Happier the man whom favorable stars
Allot thee for his lovely bedfellow. (4.5.41-45)
It's no surprise that the moment of Kate's so-called "transformation" (the moment Petruchio breaks her will and tames her) occurs when she and Petruchio transform an old man into a "budding virgin." Part of what makes Kate a new kind of person is her ability to pretend, just like an actor.
Quote 2
KATHARINA
Husband, let's follow, to see the end of
this ado.
PETRUCHIO
First kiss me, Kate, and we will. (5.1.145-147)
For once, Kate's public problems with Petruchio are no longer the main attraction in Padua. Here, Kate suggests that she and Petruchio follow Bianca and Lucentio in to the wedding banquet, to see how the new couple's "drama" will work out. Just as quickly, though, Petruchio demands that they draw attention to themselves again by making out in public. This reminds us that, although the attention has just been on Bianca and Lucentio, it is Kate and Petruchio who are the center of the story. It's also a reminder to Kate that her public obedience will always be tested by her husband and scrutinized by the public.
Quote 3
KATHERINE
Such duty as the subject owes the prince
Even such a woman oweth to her husband;
And when she is froward, peevish, sullen, sour,
And not obedient to his honest will,
What is she but a foul contending rebel (5.2.171-175)
Kate compares husbands and wives to princes and subjects to assert the hierarchical power structure in marriage. Here, she implies that the home is like a mini-kingdom, which gives credence to the idea that unruly wives/subjects threaten the very fabric of the family structure and are a kind of danger to the public.