Answer: Nothing but their children’s deaths could stop the parents’ anger.
What these lines state is that the parents' feud was continuous, and that, besides the children dying, nothing could stop it. In other words, nothing but the children's deaths could stop the parents' anger. This is true as we reach the end. It is only after the tragic death of Romeo and Juliet that the Capulet and the Montague are able to end their feud and leave their hate behind.
