I remember being wrongfully accused of something (by my mother) when I was in high school.  When she figured out I hadn't done it, she apologized.  I was feeling angry and victimized, notwithstanding the apology, until my father told me that I had lost the benefit of the doubt because of some of my boneheaded actions a month or so before.  The fact that he sided with my mother, even though she was wrong, made me even madder in the short term, but I quickly realized how much I lost through my prior actions, because I understood the concept of not having the benefit of the doubt any longer.  It was a big learning experience for me.

Maybe it's something your SO's daughter needs to learn.  Of course, it would need to come from him.

I understand you are looking for advice for this particular issue but I think there may be a lot  more issues percolating below the surface than you realize.

First, if the 16-year-old has been involved with drinking/drugs/sex, then that is a serious problem that her father (and BM, if she's around) need to address.   The girl may be having issues with the fact that you are there in the home, with your small son who needs lots of hands-on, and he is now getting attention that she feels her and her sisters deserve. 

Your SO has full custody and here you are, in a year's time, all moved in and involved in their lives.  Rightly or wrongly, those girls may very well feel that you are an invader.   

The fact you said your SO is now "building walls back up" belies your statement that your relationship with him is great and communciation is open.  I don't think it is - otherwise, he wouldn't be building walls, he'd be telling you what is bothering him. 

If you are feeling uncomfortable in the home, I would say it's long overdue.  Moving in together after such a short relationship was not wise.  IMO, you should now focus on your priorities - which is making your OWN home for yourself and YOUR son.  Then go back to dating your SO until such time as you can all figure out a way to integrate your lives better.   His priority needs to be to regaining all his daughers' trust, and you need to focus on caring for your son.  

I wouldn't feel bad about suspecting a known drug user stole your missing pills. Way back when, whenever I lost an article of clothing, I suspected my SD because she was always stealing my clothes. Never felt bad if I found it later. Wouldn't have suspected her if she hadn't already stolen so many times.

formulate the conclusion you and your  SO arrived at regarding the disappearance of your medications.

Yes, you jumped to an inaccurate conclusion. However, her historic behaviors are still pertinent to the dynamic in your home. Quit begging for the SKid's forgiveness. Just apologize and move on.  Her behavior will put this in the past in short order.  The balance sheet will right itself and make this a mere blip on the historic RADAR screen.

I would appologize and then get over it real fast. This can be a lesson to SD about her reputation. If you've been a thief before people are going to think it's you anytime something goes missing.  She's got some making up to do and a lot of trust to re earn. 

Write her an apology, since she won't talk to you.  Make it sincere, short, and to the point.  Tell her that you and she should move on and put this behind the two of you, no forgiveness needed at this time.  Then let it go and move forward.  I wouldn't beg her for forgiveness nor beg her to listen to you. 

On the other hand, you might just let it go, as you have attempted to apologize;d move forward, be civil, and let her Dad take care of her behavior in the future.  

Mistakes are made, but time usually will tell the truth.  Maybe next time, give it more time to develop.  I'm sure you've learned this.