All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that defending a Muslim and helping him/her in finding a way out of his/her difficulties is something Islamically required as the Prophet said: “A Muslim is a brother of another Muslim, so he should not oppress him, he should not forsake him but should support and protect him, nor should he hand him over to an oppressor. Whoever fulfils the needs of his brother, Allaah will fulfill his needs; whoever brings his (Muslim) brother out of a discomfort, Allaah will bring him out of the discomforts of the Day of Resurrection, and whoever conceals the sins of a Muslim, Allaah will conceal his sins on the Day of Resurrection.” [Al-Bukhari and Muslim]
As regards how to deal with that problem, then if the situation of this woman (guest) is as you mentioned in the question, and she refuses to leave, and you are unable to convince her to leave in a soft and gentle manner, then you may force her to leave or call the police, and we do not think that this is difficult to do. If her husband was able to kick her out of his home and she could not with the existing law oblige him to let her stay with him, then it is more appropriate and easier for you to kick her out. It is not Islamically an obligation to host her and the Muslim sisters should not take her as their friend.
However, the questioner did not explain to us whether this woman is a Muslim or a non-Muslim so that we may comment on her marriage with a Christian man. If she is a Muslim, then he is not her husband because it is not permitted for a Muslim woman to marry a Christian man as we clarified in Fatwa 81220.
Also, for more benefit on keeping company with a dissolute person, please refer to Fatwa 93050, and to Fatwa 88293 on the limits of dealing with non-Muslims.
Allaah Knows best.