Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
You have to know that in our religion it is forbidden to establish such emotional relationships between a man and an alien woman, because this leads to the spread of anarchy and mischief. However, if a man falls in love with a woman, then he has to hasten to ask her hand for marriage from her parents. Similarly, if a woman loves a man, then she can propose herself to him for marriage. This is the best solution for this love, to flourish. So, if this happens, then Al-Hamdu Lillahi (Praise be to Allah), otherwise you have to stop this relationship, and each one of you should refrain from thinking about the other.
You have to know that Islamicly there is no harm for a married man to marry a second wife. The consent of the first wife is not obligatory for the husband to marry the second one. However, it is more appropriate, if possible, that there is consent. And if they fear harm in case they make the marriage public, then it is permissible for them to get married secretly provided that the conditions of a correct marriage are met, like the presence of a wali, the Mahr (bridal money) and the two witnesses. But they might not make the marriage public, and it is possible that one of the partners gives up some of his/her rights, like providing for the wife, staying together with her by night and so on.
However, it is forbidden for a man and an alien woman to live together and have sexual intercourse, as this is fornication and adultery, and if there is a child from this relationship, it is a child of Zina (fornication/adultery), and the child does not take the name of the father.
To conclude, we would like to draw your attention to two important matters. The first matter is that it is not permissible for a woman to ask a man to divorce his wife in order to get married with her, as the Prophet (Sallallahu Alaihi wa Sallam) said: "No woman should ask for the divorce of her sister (Muslim) so as to take her place, but she should marry the man (without compelling him to divorce his other wife), for she will have nothing but what Allah has written for her."
The second matter is that if divorce takes place, the woman has more right to foster the child, and when the child reaches the age of seven, he/she will be given the choice to choose between his father or mother, however, there is a difference of opinion about this among the Fuqaha (Islamic jurisprudents).
In such matters, one should refer to Islamic courts of justice, because it is more appropriate for the judge to study the case, and both parties should abide by his ruling. The judge's ruling solves the problem of the difference of opinion among the Fuqaha as well.
Allah knows best.