I would never recommend such a marriage for the following reasons:

 

1. There is no room in Islam for the so-called secret marriage. Marriage in Islam has a dual nature: it is a social contract even as it is a solemn religious contract. Therefore, those who are living as married spouses must be known in the community as a married couple; so, for you to have a secret marriage is like living as a mistress. The Prophet (peace be upon him) said, “Announce marriage and publicize it by beating drums.” The purpose was to rule out any room for suspicion and gossip and protect the interests of the individual as well as the community. Furthermore, it is intended to preempt any conflicts and pave the foundation for a family based on trust and transparency.
2. A second marriage is not a right; it is rather a responsibility. Monogamy is the ideal in Islam and the permission to marry another wife is an exception granted under specific conditions.
3. I am assuming the man is living in a milieu or culture where monogamy is the norm and polygamy is illegal. If this is the case, then the woman married this man assuming that she would be his sole wife; therefore, it was a tacit agreement of his contract with her. The Prophet said, “There is no covenant whose terms are more worthy of strict compliance with the provisions of the marriage contract.” So, he is in breach of his marriage contract if he is considering marrying you without her consent and knowledge. You should ask yourself: If you were in her place would you agree to such a thing?
4. Lastly, you are wrong in forging such an illicit relationship with a married man with kids.

I would advise you against it.

Almighty Allah knows best.