How do you deal with a teenager that you are not, getting through to?

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My mom has a Teenage daughter, who she told to go to the market with her but she decided that she don't want to go and there is nothing that she can do to make her go. She is 14 years will be 15 soon but my mother don't want to leave her by herself, especially in the night. My mother call me several times out of frustration and I spoke to my sister but when I am off the phone everything remains the same. My mother is having difficulty getting through to her, not only with this incident alone but on other occasions. Should she just tell her what to do, what is right and if she doesn't listen leave her alone, how would you handle this?