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You seem to be trying very good strategies! Sometimes toddlers and young children outgrow these fears, too. Here is an article http://bit.ly/2hq5WEp which gives some good references for addressing young children's fears. Hope this helps!
Wow! This situation is confusing and would depend on the relationships of the people involved. If OP's relationship with Mom is friendly and supportive, then I might tell Mom.

My differing opinion stems from thinking what I would appreciate if OP's daughter were my own. I would want to know. Not to tell my daughter it is unhealthy or wrong, but I would want to help if her smoking is an indication of something else going on her life.

My daughter had an eating disorder in college I wish I would have known about sooner. Her friends thought it was "none of my business". I wish they would have told me.

Praying for the right decision.
You are like other people I know and they are very normal, nice people. My husband often talks about Myers-Briggs and DISC, and these personality profiling systems confirm some people are introverts and some are extroverts. I rather admire people who are content with just being themselves. You sound like a person like that! For me, connecting with people is to share my life, feelings, and faith.
From everything written, it sounds like getting an accurate diagnosis and possibly, professional help seems reasonable. Sometimes, answers to our questions are within us because we know our children and ourselves better than anyone else.

To OP, what do you believe should be the next step?
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