I can only tell you what I would do - which may not be something you can live with.
I would return her item to her and keep myself blameless.
It's true that I would be giving up my leverage in bargaining for my own stuff. But my reasoning would be that I don't want to enter into negotiations with my BPD relative because they would only see it as a way to weasel themselves back into my life - after all, I am engaging with them, am I not? - and they would draw it out and maximise the unpleasantness for me in the process. And the end result would still remain questionable.
It keeps being repeated that people with BPD are afraid of abandonment. It seems to me you'd be walking straight into a trap by entering into a fight over things your mother should return to you - as long as she doesn't, she can keep you interacting with her for as long as you keep fighting. Even she may know that it won't keep the door open indefinitely, but it will for some time, during which you will expose yourself to her manipulation again - and she may see it as an opportunity to get you back under control.
If I were in such a position, I would almost always let it go - return the item that isn't mine, ask for my own stuff back at the same time and in writing, but then disengage. That's if it is at all an option. It gets more complicated if she is sitting on something you
need (such as equipment for your job) and cannot easily replace (e.g. because it would be too costly to do so).
But in all other cases, I'd let it go. Which isn't to say I don't understand that it can be hard. It just seems like a case of choosing the lesser evil to me.
Regarding the fact that she was the person to request NC - I have some personal experience of that being a manipulation tactic. It doesn't have to be, but it was in my case. In a last-ditch attempt to establish a relationship with my sister that wasn't based on her using me and dropping off the ends of the Earth when she didn't need me, I wrote her a letter to tell her how I felt. Her response was a highly vitriolic email (potshots, guilt trips, double-binds and such) that ended with her telling me that we were better off without each other. I had suspected as much, even thanked her for her reply and confirmed that yes, we were indeed better off without each other, and ended with wishing her luck with everything she might decide to do in life. (I know it could be read as sarcastic, but it wasn't intended to be, because I really believed that those could be my last words to her.)
Contrary to expectation, she blew a gasket that I had the audacity to cut her out (despite her having been the one to say that we were better off without each other, which was really more her cutting me out at that point than me cutting her out).
We are now NC, but not without her having tried to get me back to interacting with her - first by trying to rope me into fights, then waiting a while and writing me emails as if nothing had happened, trying to get us to meet up, which I still responded to by declining politely but succinctly. After a while, she stopped, which led to the current NC.
Btw, I wouldn't classify my sister as fully BPD but rather more NPD. But I think the principle she was acting on could still apply to situations that involve people with BPD.
I just thought I would mention this with regard to your mother's request to go NC, which can initially seem strange for someone with BPD, but doesn't have to be when you consider that it could (sadly) just be a tactic.
Sorry - this turned out rather longer than expected.
