Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
We advise this woman to make repentance due to violating the ruling of Shariah by traveling alone. Ibn Abbas reported in a sound Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said while giving a sermon: "No man should ever stay in seclusion with a woman unless in the presence of a Mahram of that woman. And no woman should travel unless accompanied by a Mahram." A man stood up and said: chr(39)O Prophet of Allah! My wife went on Hajj and I have already been registered for the Ghazwa of such and such.chr(39) Thereupon, the Prophet (Sallallahu Alaihi wa Sallam) said: "Go and perform Hajj with your wife." [Reported by Imams al-Bukhari and Muslim].
As for living in your house, it is forbidden for a woman or a man to stay in seclusion with a member of the opposite sex. However, if your house is large enough so that she can live in one of the rooms that has all separate facilities such as a toilet passage, etc. then it is permissible. Ibn Hajar al-Haithami said: chr(39)If a woman lives in a room beside or upstairs or below the room of an alien man, the facilities such as kitchen, toilet, passageway, terrace, etc. should not be shared between them. Living in an accommodation sharing the above facilities is forbidden, because more likely it causes mixing, and being in seclusion with each other which are forbidden in Shariah. If they have separate facilities from each other but there is an open door between them or the door of one of them opens into the otherchr(39)s room or the passage is through the otherchr(39)s room, living in such a place is forbidden.chr(39)
Now, if she lives fulfilling the above conditions then there is no harm to let her live with you; otherwise, you have to tell her through your wife that the Shariah does not allow her to live with you for the above mentioned reasons. You should inform her husband of the truth and convince him that the rulings of Shariah are more entitled to be respected. Meanwhile, you may let her live with you till she or her husband can manage an accommodation for her provided you lower your gaze and never stay with her in seclusion during this period.
However, whether she lives with you or not, if you come to know of her bad practices you have to prevent her from doing so by suitable means. However, you are not her Wali, i.e. she is not obliged to obey you or listen to you. Allah knows best.