What do I do to stop my female zebra finch from biting the males feathers?

The male was the first in the cage. Then I bought him a companion and they seemed to like eachother for a few months. They had eggs, but no chicks. And after she delivered the eggs, the birdie-girl started to bite the other one. Poor little bird had a bare neck for a few time. We thought about separating them, but my mom says two cages dont look good, so she thinks about giving the female to a shop for free. I know finches need company and I told her so but she told me shes scared the other one will bite him too. Is there any way to calm the young lady, so they will get along well like in the begining?