I would say that she should retake the class. It isn't traumatic, at all. My first semester of high school, I was in advanced Algebra 2. I got a D in it because I didn't understand anything! The second semester, I dropped to Algebra 1, and I ended up getting an A, I think.
Another story: My junior year of HS, I took two semesters of Geometry. I did very poorly- I got a C both semesters. Mostly, this was because I didn't pay attention enough. I ended up retaking it during the summer, and I got two As.
I was very proud of myself, and the class was much easier since I had taken it before AND because it was the only class I was doing during the summer!
If your daughter is planning on going to a good university, she should retake the class. Even if she isn't, a C in high school is like a D or F in college- it's just not good, even if it IS considered "passing." Also, if she is an advanced student who "likes" to get good grades, she most likely would feel worse keeping the C on her transcript than retaking the class during the summer.
I would say take my advice on this matter, because I just graduated high school last year, and it sounds like I was very much like your daughter my freshman year.