So to put it concisely the conflict with your sister-in-law can be summarized as this: The door to your sister’s room (in your house) made noise that you found annoying, her boyfriend came down shirtless and you made a comment of front of her parents that embarassed them, and then blamed her for the comment you made?
I mean, yeah, of course you’re going to have conflict with that whole family now. And your husband isn’t really doing anything to help navigate this.
Your dislike of your sister-in-law is poisoning your relationship with the mother-in-law, and you cannot seriously expect the mother-in-law to choose you over her own daughter. So you need to make peace with your sister-in-law, or abandon hope of a relationship with your MIL.
For what it’s worth, the way you describe it here, your sister-in-law sounds like she’s acting like a normal 20 year old. She’s doing things that are mildly annoying at best, and you came down way too hard on her. Maybe there’s a pattern of behavior that you haven’t mentioned here, but if the worst thing they did was make too much noise because of a problem with your door, well, they aren’t the assholes here.