I was at a relatives house and watching the kiddies play hide and seek in their wardrobe (being very cute). When I went to stop them pulling out all the neatly laid clothes I found the biggest stash of strong painkillers prescribed to the relative. I probably wouldn't have paid too much attention to it but given this relative is a recovering alcoholic/prescription addict, I packed up the kids and left. Not before I took a photo as proof.
I wasn't snooping at all, but I found them accidentally and decided to investigate further given the personal circumstances. I did confront the relative the next day.
I am just playing devils advocate here, I do think what you have uncovered is a gross breach of trust. Is it possible that she did find them accidentally and only took that information because she was genuinely concerned? I know you said there is nothing to be concerned over, but obviously she thinks differently?
Edit- this relative did babysit on occasion, which is the reason I felt it was my right to act as I did. It was my place given she was to look after my child.
I'm not saying it's your MIL's place at all but I would need to know her motivation for her actions before I decided what to do next.