You behaved rudely here, and then when your MIL tried to talk to you about it, it got worse. It sounds like she wanted you to apologize / admit some fault, and you escalated an argument.
Look, you’re 28 and the SIL is 20. For most of the time you’ve known her, you’ve been an adult and she’s been a child. Don’t get into conflict with kids. You two are not on the same level or status. The burden is on you to be mature, polite, smooth things over, etc. Your MIL asks for your help with things precisely because of that difference, where you’re a married woman and her daughter is a kid.
You were super rude with the situation that happened at your home. They were your guests. You should have taken your cues from your MIL, who ignored it. If she wasn’t ok with them sleeping together, she wouldn’t allow them to stay in the same room. She gets that they have sex. It’s not their fault the door was faulty and made noise. It wasn’t nice to ask your husband to go interrupt them and then for you to embarrass them. And then when told you made them feel bad, you should have apologized. They really didn’t do anything wrong in the first place.
I think you need to humble yourself and have an apologetic convo with your MIL. Blame hormones if needed. She needs to know that you get it and want to smooth things over.