I have no idea if this will work or not, but I'll tell you my personal story:
When I was in college years ago, I had my 1st set of tips put on my nails for a sorority formal. The woman in the salon cut all of my cuticles as she was going through the process of putting on the fake nails. Weeks later, I noticed that I had warts around every single nail bed on both hands. As a nursing student, I knew that was not going to be the hands a patient would want to have touching them when I was in the hospitals for clinicals.
I showed them to my clinical instructor, a nurse, and she gave me this advice:
Buy a bottle of Vitamin E capsules from the drugstore. Stick a pin in a capsule and squeeze out the vitamin E liquid on the warts and cover with a band-aid. Use as many capsules as needed to completely cover the warts. I did this at night every night for a month and they were gone and have never returned!!
I hope this works for your daughter, too - at least Vitamin E is not a chemical and is very safe for you to try on your young daughter. Best wishes!!