Am I obligated to tell my friend the truth about my brother's wife, whom she considers an example of piety, or would I be committing a sin by doing so?

There is a need to differentiate between sins and disliked acts. Some actions of your brother's wife – if true – such as neglecting the rights of her husband and children, are forbidden (haram). As for her serving her father-in-law, it is commendable (mustahabb) but not obligatory.

It is not permissible for you to inform your friend of your brother's wife's shortcomings without need, as this involves revealing her secrets and seeking out her hidden faults, which is forbidden. This is in accordance with the saying of the Prophet (peace be upon him): "O you who have embraced Islam with your tongues but into whose hearts faith has not entered! Do not hurt Muslims, nor revile them, nor seek out their hidden faults. For whoever seeks out the hidden faults of his Muslim brother, Allah will seek out his hidden faults, and whoever Allah seeks out his hidden faults, He will expose him, even if he is in the innermost part of his house." (Narrated by Al-Tirmidhi). Seeking out hidden faults means searching for them or revealing what is known of them.

Exposing the hidden faults of Muslims leads to great harms, including disheartening the sinner and encouraging them to persist in sin. This is based on the Prophet’s (peace be upon him) saying: "Indeed, if you follow the hidden faults of people, you will corrupt them or almost corrupt them." (Narrated by Abu Dawud). The Shari'ah encourages concealing the faults of Muslims, as the Prophet (peace be upon him) said: "Whoever conceals a Muslim's fault, Allah will conceal his fault on the Day of Resurrection." And his saying to Hazzal: "O Hazzal, had you concealed him with your garment, it would have been better for you."

This action also involves forbidden backbiting (gheebah), which is mentioning a person in their absence in a way they dislike, as the Prophet (peace be upon him) said: "Backbiting is your mentioning about your brother what he dislikes." (Narrated by Abu Dawud).

Treat people as you would like to be treated, for the Prophet (peace be upon him) said: "And let him do for people what he loves to be done to him." (Narrated by Muslim).

An exception to this is a situation where harm will come to your friend, such as if she is about to engage in a transaction with your brother's wife, and you strongly believe she will be harmed. In such a case, it is permissible to warn her only to the extent necessary to avert the harm, without elaborating on the shortcomings.