I can relate to that so very well. I had the same problem when I had your daughter's age. But... remember that I am talking about 1971...! My parents were very conservative, and when my obstetrician told them that taking the pill was the only way, my dad just became hysterial. Luckily, my mom could talk some sense into him, so I got "the pill" when I was 17. I had to swear not to take "advantage" of this . No worries, I was a good girl !
Since then, I didn't have any more problems. I was happy again
After we got married, we wanted to have kids, so I had to stop with that pill. The cramps came back and often kept me home from work.... .
We didn't get any kids of our own though... .
Since about 15 years, I am taking the pill again, as those cramps were so unbearable that I had to stay in bed every time. Now, it is all better again.

My advice: let your daughter take that pill. She won't be feeling so miserable again. I know it will make it easier for her to have sex, but at least she will be so much happier. Don't worry, she will be be very thankful for your trust!