Feif Un is correct. In fact, non-Jewish women “married” to Jewish men convert *all the time.* Much of the time the convert is the one who in effect mekarevs the Jewish husband, but it can happen the other way around too. If a man who is making teshuvah is married to a non-Jew, he should teach her about Judaism, include her in the kiruv and other Jewish activities he is involved in, have her read books, etc. Give her some time. There is no need to rush.
If within a few months it is 100% clear that she is hostile to or completely uninterested in becoming a completely observant Jew, then divorce may be needed. But in many cases, the spouse ends up converting, along with the children — which is quite a simple matter if they are under bar/bas mitzvah age and can be enrolled in an Orthodox school. As long as she is committed to remaining an Orthodox Jew even if the marriage ends, then the conversion is kosher.
If I knew someone involved making teshuvah whose kiruv rabbis were telling him to divorce her immediately and that conversion is not an option, I would tell him to run away from them and finish getting mekareved by someone else. Divorcing her immediately, especially if he loves her, is like playing G-d. How do we know Hashem does not want her and the children to convert? Rahab was a prostitute before she converted, but she merited to be the ancestor of prophets.
If he does divorce her, Hashem forbid he should shun his children and never see them again! How disgusting. Popa, can you cite a single psak that a man in this situation should do this? Derech eretz kadmah l’Torah.