I smelled cigarette smoke smell on my helper after she came back on her off day. Should I confront her? Can I ask her to quit if she admits?

Personally, if I were you, I would ask if she has a habit of smoking. While I don't think there is a way to mandate her to quit, I would state clearly that I would not want her to smoke while working, especially when she is handling the children. It could be that she was just around some smokers. So I think it is best to clarify by asking her directly.