All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The scholars stated that among the etiquettes of a learner is that he/she should respect his/her teacher and he/she should be keen on pleasing him/her even if this is against his/her desires. An-Nawawi said: “Among the etiquettes of a learner is that he should endeavor to please his teacher even if this is against his own opinion…….He should greet with Salaam all the people present (audience) with a loud voice to make everyone actually hears him, and he should especially treat his Shaykh (teacher) with additional respect.”
Besides, Al-‘Adawi from the Maaliki school of jurisprudence, quoted one of the scholars as saying: “The student of knowledge should be humble to his Shaykh and he should have a good conduct with him even if he [i.e. the Shaykh] is younger than him, and is less famous than him and is of less noble lineage than him.”
Therefore, if becomes clear that that student should respect you as a teacher even if you are younger than her.
On the other hand, you should honor her for her old age. Anas said: “An old man came wanting to see the Prophet and the people were slow to make a way for him, then the Prophet said: ''He is not one of us he who does not have mercy towards our youngsters and does not respect our elders.” [At-Tirmithi]
However, if you order her to do something related to the study, then it is your right on her as a teacher that she obeys you, and her saying that she is older than you is an inappropriate argument from her side.
Hence, we advise you to be patient with some harshness or rudeness that you may encounter from your students, as there is good in being patient. An-Nawawi stated that among the etiquettes of the teacher with his students is that he should be patient with their harshness and misconduct.
Allaah Knows best.