I had the same problem, only difference it was a cockerel that pecked my lip. He also pecked other peoples lips. All you had to do was get close enough and he would jump up and peck your mouth. It only took one peck to break skin. He broke my skin twice in two different occasions. That's when I realized he had a problem with healthy looking lips.
I didn't stop handling him though, I would always be prepared and tuck my lips in every time he would get close. He was a little mean to his siblings as well, therefore, I would isolate him outside the coup for a few hours. He always wanted to get back in with his brothers and sisters. As he grew up, it didn't seem to be a problem any more. But I did sell him along with 6 other cockerels. Unfortunately I could only keep 2 roosters.
I would suggest to either sell the mean chicken, make soup, or don't have your daughter get close to that chicken. Perhaps separate your mean chicken outside of the area where your daughter is interacting with the rest of the flock. Chickens are very social animals, therefore separation does kind of teach them a lesson. Make sure the mean hen can see the rest of the flock with your daughter and if she wonders off, that's ok too. Just retrieve her once you and your daughter are done interacting with the flock. Hope this helps.
