Is the home rightfully the first wife's or the second wife's, if the first wife left her home out of anger, and the husband married another woman whom he housed in the first wife's home, then the first wife returned and demanded her home back?

If the house is owned by the husband, he may assign it to either of his wives, provided it is suitable for her circumstances and his means. He must provide the other wife with a separate dwelling befitting her; for a separate dwelling is a right of the wife upon her husband. If the husband provides this dwelling, the wife is not entitled to refuse to live in it without a legitimate Sharia (definition)-compliant justification.