Cheating on her husband and having such a relationship is totally prohibited in Islam. You are sinful for trespassing over the rights of such a husband even if he is a Kafir.
Premarital relationships are prohibited in Islam. In many of the hundreds of cases that I have seen, similar marriages ended up in separation, the wife running away with the children and making them Christians as she was never really convinced or committed to Islam.
There are thousands of Muslim women who are available for marriage if you want something that would please your parents, raise your children and know your culture well