What are some of the challenges Orgon faces as the sole "ruler" of his household with his daughter, wife, brother-in-law, and servant?
The reality is that Orgon creates most of the challenges he faces, because he blinds himself to the truth by refusing to listen to the family members in his household, choosing instead to listen to his mother's advice and Tartuffe's advice. Orgon decides to let Tartuffe stay based on the advice of his mother. Orgon is responsible for Marianne's marriage; he chooses Tartuffe over Valere (a poor decision since she loved Valere and Tartuffe turns out to be a fraud out for money, property,and women. Orgon chooses to ignore Valere's true piety, in favor of the distracting displays of religious fervour shown by Tartuffe. Orgon chooses not to believe his wife Elmire and son Damis, who believe Tartuffe disreputable. He hastily casts out Damis, and refuses to believe Tartuffe has "put the moves on" Elmire. Orgon chooses to sign his estate over to Tartuffe, based on Tartuffe's advice. Tartuffe ignores Doris's advice as baseless, even though she sees more of what is going on than he does. He also ignores Cleante's attempts to open Orgon's eyes to Tarrtuffe's false pretenses. Orgon chooses to handle the challenges by deferring all his faith and trust to his mother and Tartuffe; big mistake.
Probably not since the servant, Dorine, seems to be somewhat out of control; afterall, as only a maid, she does not hesitate to speak up to the grandmother in the very first act. Her retorts to Tartuffe are those of a person of higher status: she is caustic and impertinent as though she is an integral part of the family (Act III, Scene II).
Also, as the grandmother leaves the house in Act I, there seems to be confusion over who has been in charge of affairs: "I leave your house, I tell you, very ill edified; my instructions are all contradicted." Should not Tartuffe be giving the instructions?