Would the wife be sinful if she did not warn the other wife about her husband who is negligent in prayer and consumes forbidden things?

It is a religious obligation to conceal the faults of a Muslim who commits a sin, unless he is known for committing major sins and having bad character, and he intends to engage in a transaction with someone, such as a marriage contract or a partnership. In such a case, it is obligatory for whoever knows his true condition to advise the other party and clarify to them the reality of this man. This falls under the category of obligatory advice and is not considered forbidden backbiting (gheebah). The evidence for this is the saying of the Messenger of Allah (peace and blessings be upon him): "Religion is advice." Ibn Hajar Al-Haytami said: "It is obligatory for a stranger who knows of a defect in an item to inform the one who intends to acquire it... just as it is obligatory for him if he sees a man proposing to a woman and knows of a defect in her or him, or if he sees a person intending to associate with another for a transaction or friendship..." Ibn Baz said: "This is not from backbiting nor from tale-bearing, but rather from giving sincere advice for the sake of Allah and His servants." Sheikh Ibn Uthaymeen said: "Concealing the wrongdoer, if his concealment increases him in evil and deeper immersion in aggression, then concealing him in this case is impermissible." Therefore, it is the right of the second wife upon you that you clarify the husband's situation to her. You must strive to control yourself so that your motive for this clarification is not jealousy of the second wife, but rather that your incentive for doing so is purely sincere advice for the sake of Allah. You should also use wisdom in giving this advice so that it does not appear that you are doing so to harm her.