What is the best course of action towards my fiancée who violated our agreement by wearing makeup, having done so before despite my warning? Should I inform her father or break off the engagement?

What we advise you to do is to explain to your fiancée the obligation of covering up and the impermissibility of displaying adornment to non-mahram men. If that does not work, then inform her father to prevent her from adorning herself when going out. If she does not respond and remains in that state, then it is permissible for you to marry her. However, at that point, based on the husband's guardianship, you must prevent her from adorning herself for non-mahram men. It is permissible for you to break off the engagement, and that is not obligatory upon you, but breaking it off might be more appropriate if it becomes clear to you that her religious commitment is weak and her response to advice is poor, knowing that the fiancé is a non-mahram to the fiancée; it is not permissible for him to be alone with her or to engage extensively in conversation with her without a necessity.