Acutally, oftentimes the addiction has something to do with the mental illness; it's that person's way of self medicating their pain away.
I wish I knew what to tell you about the situation with the shop owner. Is this shop owner a friend of yours, or just an acquaintance? If you are comfortable talking to him or her about the situation, go for it.
I don't know that there's really a right or wrong to this one, because your daughter will still do whatever she wants to do regardless. If she doesn't steal from the shop owner, she'll just find another way to get that money, and the other way will probably do your reputation no favors either.
I know this was the most ambiguous answer I could have given; maybe the old saying of let go and let God applies?