When an adult child of ours, living in our house steals, and we confront them, how do we treat them at the time of the confrontation and afterward whether they are in the house or decide to leave? What should the appropriate treatment of that child be?
When an adult steals, you call the police to report the matter. "For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same. For he is God's minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God's minister, an avenger to execute wrath on him who practices evil" (Romans 13:3-4). He is an adult, he made choices, and he is responsible to live with the consequences of those choices.
You have him leave the house. The person did not treat his own parents with respect, so he is not to be trusted to be in the home. "Honor your father and mother," which is the first commandment with promise: that it may be well with you and you may live long on the earth" (Ephesians 6:2-3). When someone violates the laws of God, remaining in sin, you separate yourself from the sin. "But now I have written to you not to keep company with anyone named a brother, who is sexually immoral, or covetous, or an idolater, or a reviler, or a drunkard, or an extortioner--not even to eat with such a person" (I Corinthians 5:11).
There shouldn't be any yelling or screaming, but there can't be any tolerance or excuses for sinful behavior either. "But avoid foolish and ignorant disputes, knowing that they generate strife. And a servant of the Lord must not quarrel but be gentle to all, able to teach, patient, in humility correcting those who are in opposition, if God perhaps will grant them repentance, so that they may know the truth, and that they may come to their senses and escape the snare of the devil, having been taken captive by him to do his will" (II Timothy 2:23-26). Understand that stealing is probably a sign of deeper problems, such as drug addiction or a gambling problem. There is a motivation behind the stealing and that should be sought.
Perhaps one day he will repent of his sin and your relationship can be renewed. But in the meantime, the best thing you can do for him is to firmly stand against his sin.