Act 3 continues both main plot and subplot, but I find myself little interested in the wooing of Bianca. 3.2 is a crucial scene. When Petruchio does not show up for the wedding, we are not yet clear that this is part of his “taming” plot. Why does Kate “exit weeping”? Does this mean that she has been publicly shamed, or that she had become attracted to Petruchio? A director has a lot of latitude here, and could play it all for easy laughs, or could suggest that more is going on. Shakespeare’s words don’t give much away, and have to be embodied by good actors, who convey feeling in other ways. We then pause while Biondello preps us for Petruchio’s entrance in old clothes — which turns out to be the second stage of his “taming” plot — but I think he goes on too long. Maybe this was designed as a comic bit for a skilled comic actor. Petruchio blusters his way through the scene, and I think we catch on and laugh with him. The real question is: what is Kate thinking? How does an actor play her? Is she fuming? Is she softening?
I am guessing that we only get a report of the wedding ceremony, which Petruchio unceremoniously disrupts, because Shakespeare thought we got enough of Petruchio’s “act” in the wooing scene in 2.1 and because he wants to top it all with Petruchio’s exit speech, carrying Kate off (maybe literally) as “my chattels.” His language listing his chattels is so over the top — “my horse, my ox, my anything” — that even today’s feminists would have to laugh. The scene remains a comic one, and is treated as such by Gremio and Bianca and the others left on stage.
Act 3 encompasses the wedding of Petruccio and Katherine, though it happens offstage near the end of scene 3. When Katherine exits weeping, it seems in response to Petruccio’s not showing up for the wedding when all the rest have come. She thinks he does not mean to marry. Does this mean that she has reconciled herself to the marriage? Sh. doesn’t give us much to go on for her feelings here, but as you say, it gives the actress playing Katherine some scope. Biondello’s description of Petruccio looks like a comic set piece, and of course it prepares us for his actual appearance “fantastically dressed.” Everyone tries to persuade him to put on proper clothes, but it’s clearly part of his purpose to continue in his mad costume. Apparently Katherine accepts this — or has no choice. Her second trial is Petruccio’s resolve to not participate in the marriage feast, and to insist that Katherine come with him on his sudden leaving. His speech about Katherine being his goods and chattels seems harsh, but then he pretends that thieves wish to steal Katherine and he orders Grumio to protect her. He suddenly becomes chivalrous, though in the event he’s the one taking her.