I didn't think they let you teach English without at least one Tolkien book under your belt.
Try telling her about the growing academic study of Tolkien and the fantasy genre - you realize some places will award you a master's degree in Tolkien Studies? Or that Tolkien himself was a widely accomplished scholar of Anglo-Saxon and early English literature? There is even a journal out of West Virginia University Press that specifically publishes academic Tolkien criticism! His works draw on major literary themes inspired by northern European, Norse, Anglo-Saxon, and Irish epic poetry, mythology, and culture - there is so much to learn in them, not to mention his impeccable use of the English language.
Fantasy is a legit genre - and an important one! Quite possibly more important than realistic fiction as a whole! Where is my evidence? I don't know, because that is just my opinion, but I really think reading the Hobbit in class is a great idea and I want to help you convince her to do it!