What is the ruling on living in a house, one-third of which was purchased with ill-gotten money, knowing that its owner is regretful and wishes to repent, and lives in it with his children?

I praise Allah the Almighty for guiding you to repentance and commitment. If a Muslim acquires unlawful wealth, such as a bribe, and is unable to return it to its owners, or is ignorant of them, or if they have already received an illicit benefit in exchange for the bribe, then he must spend it on charitable causes and public welfare projects for Muslims, if the money is still available. If he spent it during his lifetime on food, housing, and the like, then he must donate an amount equivalent to the money if he is wealthy. However, if he is poor, he is not burdened with this, and his sincere repentance suffices him. The issue concerns your personal liability, not the house you live in.