My daughter has pain in her back that radiates to her side. It is on the left, and there is a history of kidney stones in our family. Should I worry?

Might need analysis. The symptoms your daughter is describing are typical for kidney stone so this is a possibility. Almost always, there will be blood in the urine when this happens so she should collect a specimen for this unless the blood is so much you can see it (urine should be clear), she should see her personal doctor if this persists. Should you worry? Well you are her mom and she may need your help.
See a doctor. See a doctor kidney stones cause pretty bad pain and if there is blockage of the flow from the kidney to the bladder it could damage her kidneys.