Responsa Mi'lamed Li'hoil 2:83

The question is apparent from the answer. It is clear from the Shulkhan Aruch (Y”D 268:12) that we do not accept converts who do so motivated by marriage…The Beit Yosef writes that ultimately, discretion is given to the court in deciding when to accept converts. If the court is certain that the convert is converting ‘for the sake of heaven’ even if the convert is also motivated by marriage, it is permitted to accept the convert. In our case, where the Jewess already had a civil marriage, and she is pregnant from him – it is clear that they will remain married even if he doesn’t convert. If so, there is a strong presumption that he is converting for the sake of heaven. If we do not accept him, she will remained married to him thereby transgressing a biblical (de-Oraita) prohibition, as a Jewess is forbidden to a Gentile by the Bible. Hence, it is better for us to accept him than for her to remain in a forbidden marriage. Now, if the objection should be raised: ‘We do not tell a person: “Sin so that your fellow may gain” — why should the court infringe the law and accept for conversion a Gentile who is not motivated “for the sake of Heaven” in order to save the woman from a greater transgression whereby her whole life is in sin? Why, it is she who initiated the sin! The answer to this is: First, although she began to sin in free will, by abandoning herself to a Gentile, nevertheless now she is in a state of coercion, because she is pregnant by him and cannot stand the shame of not marrying him. And she is afraid that no one will ever marry her in the future, and she will have to remain single for the rest of her life ...Furthermore, if she remains married to the gentile, her children, although legally completely Jewish, will be drawn after the gentile ways of their father and sin, and these sheep how did they err? Therefore, it is better that the court do a minor sin and accept the convert and familiarize him with Judaism, so that the children will be saved...