What is the religious ruling on a husband's refusal to allow his elderly, homeless father-in-law to stay with his daughter? And must the wife obey her husband in this situation?

It is commendable for your husband to accept your father living with you in your home, as this falls under aiding Muslims and fulfilling their needs. However, if the husband insists on refusing, it is not permissible to object to him. The questioner should exert her effort in assisting her father; if he has no money, she should give him some. If she herself has no money, then whoever is responsible for his maintenance should provide him with housing, bearing in mind that obedience to the husband takes precedence over obedience to others.