Am I obligated to reveal the fact that the girl's mother allows a young man into the house and permits her daughter to go out with him, given that I learned of this situation from an external source?

The daughter who goes out with a foreign man, and her mother who allows him into the house in her husband's absence, should be advised kindly and reminded of Allah Almighty. If they do not desist after advice, they can be threatened with informing the father. If the threat is unsuccessful, the father should be discreetly alerted to be wary of this. The Prophet, peace and blessings be upon him, said: "And a woman is a guardian in her husband's house and is responsible for her charge," and "You have the right that they should not allow anyone into your beds whom you dislike."