Is it permissible to continue an emotional relationship with a married man who has three children, despite both of them knowing the impermissibility of this relationship and their desire to marry, but circumstances prevent it?

If you are afflicted with love for a man who is not a mahram (definition), then there is nothing better than marrying him, if possible, while observing fairness if he is already married. However, if it is not destined to be, then you must conceal the matter, practice chastity, be patient, and seek reward from Allah. Divert your thoughts from this man, avoid him, and stay away from mixing with non-mahram men. If it requires leaving your job, then do so. If a man of religion and good character proposes to you, marry him immediately to protect yourself. You must also supplicate and seek Allah's help to cure you from this ailment.