You can asked her if she was smoking or was she with someone who was smoking. Ask it casually and nice, so that if she is smoking, she wouldn't lie to you about it. If she was smoking, tell her that she needs to quit as she is handling your kids. Offer her help if she finds it difficult to kick the habit. If it was someone around her who was smoking, ask her to shower and have a change of clothes before handling your kids of hygiene purposes.
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.
Not sure if this is within your control. Is her off day and smoking is not illegal per say. I personally suggest you ask if she smokes on her off days. If she is doing so, just set the rules that she can't smoke on normal days and she has to bath after reaching home from off days.
Maybe she met a friend who happened to be a smoker? Give her the benefit of the doubt. You can ask her if you're feeling uneasy. If she admits it, then it's up to you whether you are comfortable with the fact. I wouldn't, if she has to be around my children.
I think you should confront her since she will be taking care of your kids and likely you will not want your kids to be exposed to cigarettes. If she admits that she smokes, you have the rights to ask her to quit or change another helper.
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thanks