What is the ruling on a woman who does not perform ghusl after intercourse, whether out of ignorance or negligence, and is the questioner sinful if he does not hint to her about performing ghusl?

You must teach women the obligation of performing ghusl (ritual bath) after major ritual impurity (janabah), as this falls under enjoining good and forbidding evil. Hinting at the desirability of ghusl is not sufficient, because ghusl requires the intention of purifying oneself from janabah, not merely cleaning oneself. Modesty should not prevent you from enjoining good, for the Messenger of Allah, peace and blessings be upon him, said: "None of you should belittle himself from seeing a matter concerning which Allah has a say, and then not speaking about it. Then Allah will say: 'What prevented you from speaking about it?' He will say: 'My Lord, I feared people.' He will say: 'And I am more deserving that you should fear Me.'" And whoever seeks the pleasure of Allah through the displeasure of people, Allah will suffice him against the burden of people.