Is it permissible for a mother to eat chicken she raised at home after having previously forbidden herself from eating it because she saw it eating filth, and is expiation required if she eats from it?

Prohibiting what Allah has made lawful, such as chicken and the like, is an idle utterance that carries no obligation. The madhhab of Malik, Shafi'i, and the majority of scholars is that saying "this food is forbidden to me" or any other statement prohibiting anything other than one's wife or slave-woman is an idle utterance, and nothing is entailed by it. The forbidden item does not become unlawful to him through such a statement. Therefore, there is no blame upon your mother for eating chicken, and no expiation is binding upon her. She should, however, not repeat such an action.