Just because your internship ran aground does not mean that you should delete it from your resume. A resume is supposed to be a truthful summary of your prior work experiences, and employers do not appreciate reading fictionalized accounts. In fact, if you are hired and the company finds that you presented false information during the hiring process, you will most likely be terminated.
As you indicated, the internship is a "great addition" to your resume. If you cut it, you are also cutting your marketability to a potential employer. In a word, you should definitely put it on your resume. When the subject of this internship comes up during the interview, tell the interviewer exactly what happened. You can prepare him or her for a less-than-glowing reference, and its impact will be lessened because you will have established a more positive framework in which it can be interpreted.
Several studies have found that admitting prior job problems is often interpreted by interviewers as a sign of confidence. Showing confidence to the interviewer makes more sense than trying to con the interviewer.
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