Is the marriage considered valid if the wife does not reside in the marital home, and does sin result from this?

May Allah reward you for bringing that woman into Islam. A valid marriage has conditions, the most important of which are the guardian (wali) and witnesses. If a condition is missing, the marriage is invalid and must be renewed. A Muslim woman who has no guardian is married off by the judge (Qadi); if that is not possible, she delegates a Muslim man. It is advisable to consult a scholar or the Sharia (definition) court to clarify the ruling. If the marriage is valid, there is no harm in the wife living in a safe place and the husband in another, as long as none of her rights are diminished. Justice must be maintained between wives concerning lodging and maintenance, unless one of them voluntarily waives her right. A Muslim must inquire about the Sharia ruling before undertaking an action. The first wife's knowledge or consent is not required for her husband to marry another.