If my child is choosing idolatry and living in my home, what are my obligations?
It is not clear what exactly your child is doing. Is he/she bringing idols into the home and worshipping them? In a public or private way? Is it effecting other children or may it in the future?
This is a very delicate question, but generally if the child is not harming others by his practices, keeping them at home and providing love, support and encouragement is usually the best and sometimes only chance of bringing them back to Judaism. Not to make your home “hefker” [a free for all] but to give the room needed to let them get past this difficult stage.
If the child is harming or potentially could harm other children with his actions, this is a different question. You need to consult with a Rav who knows you and your family dynamic well, and who can consult with a Gadol BaTorah to determine the best course of action.
Much Hatzlacha with this difficult nisayon.