Will sending my adolescent child away to another city (changing her environment and her company) help to get rid of the addiction?

Maybe. Sometimes these habits are a result of the social environment children stay in and they may find it easy to give up if you move to another city. But this is true only for those who are not slaving to the habit. Someone who is deep into the addiction will make friends with addicts and find places to procure the stimulant/depressant that he is addicted to, even in a new town. The answer lies in getting professional help, not in moving to a new city.