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.
First of all, we ask Allaah to make for you a way out from your distress and rectify and guide your husband.
We advise you to supplicate Allaah to guide your husband and make him hate sins and acts of disobedience. It would be useful if you advise him repeatedly in a soft and calm manner while clarifying to him that this matter is forbidden and abominable as far as Sharee’ah and human nature are concerned. How can he do this with daughters of other people while he does not accept this for his own daughters, and not even for one of his female relatives?
For instance, you may remind him of that young man who asked the Prophet to give him permission to commit Zina (fornication or adultery), as this story is deterrence to any rational person. Abu Umaamah said: "A young man came to the Prophet and asked him to give him permission to commit Zina. When the Companions heard this, they rushed to deter him and told him: “Stop it.” Then, the Prophet said: ''Bring him close to me.” Then the man got closer to the Prophet and sat down. The Prophet asked him: ''Would you like this for your mother?” The man said: “I swear by Allaah, no; may Allaah make me ransom for you”. The Prophet said: ''People do not like this for their mothers as well.” He [Prophet] asked him: “Would you like this for your daughter?” The man said: “I swear by Allaah, no, may Allaah make me ransom for you”. The Prophet said: ''People do not like this for their daughters as well.” The Prophet asked again: “Would you like this for your sister?” The man replied: “I swear by Allaah, no; may Allaah make me ransom for you” The Prophet said: ''People do not like this for their sisters as well.” The Prophet asked again: ''Would you like this for your paternal aunt?” The man replied: “I swear by Allaah, no; may Allaah make me ransom for you”. The Prophet said: ''People do not like this for their paternal aunts as well.” The Prophet asked again: ''Would you like this for your maternal aunt?” The man replied: “I swear by Allaah, no; may Allaah make me ransom for you”. The Prophet said: ''People do not like this for their maternal aunts as well.” [Ahmad]
It should be noted that if one of his children discovers this conduct from him, he would despise him due to this. Worse than this, he might imitate him in this regard, and so, he will be lured by the devil to commit Zina as well. If this happens, it would be a big shame.
Moreover, we advise you to preoccupy your husband with what is beneficial and useful, and you should beautify yourself to him so that he would not be attracted to other women.
Besides, you should know that it is forbidden in religion to follow other people’s faults. Ibn ‘Umar narrated that the Prophet said: "O you who are Muslims by tongue but ‘Eemaan (faith) has not entered your hearts! Do not harm the Muslims, and do not degrade them and do not pursue their imperfections, because if someone pursues the imperfections of his Muslim brother, Allaah will pursue his imperfections, and he whom Allaah pursues his imperfections, He would disgrace him even in his own dwelling.” [At-Tirmithi] If this is in regard to the people in general, then it is more confirmed in regard to the husband.
In any case, if your husband does not rectify himself, and you fear that your hate to him would cause you to be negligent about his rights, then you may ask for divorce even in return for compensation. There is no good for you in having marital relationship with a man who has an affectionate relationship with a non-Mahram woman and insists on this. As regards the children, Allaah will take care of them.
Allaah Knows best.