I had an email exchange and interview with this professor and I feel like I should tell her I've been accepted elsewhere to my first choice program, but writing the words down and getting the tone right are hard.
Yes, that's a hard letter to write. But she will have gotten letters like this before. Thank her, say you would have enjoyed working with her but that you have found another position that suits you better or better fits your interests.
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Write her soon, so she can offer the job to someone else.