As salamu ‘alaykum…
Dear brother, one wonders what was most on your mind when you got involved a married woman.
Even if you were just a shoulder to lean on, a person with home to share her troubles, the reality is one that you know quite well, and that is you have helped to create this situation which you have found yourself in. What did you think would happen? Did you think that nobody would be hurt if kept secret, because it would end? Were you both so consumed by your feelings that you found yourselves unable to think of nothing and nobody else. If you were the husband or the child, how would you feel?
The depth of this wife’s feelings for you has been fed by your willingness to allow this relationship to take place. Maybe you never thought that it would go this far, but it has, and could not have reached this point without you. Regardless of who approached whom, you are single and free, and she has a husband, and children to whom she is accountable to. She is not as free as you think you are, and you have encouraged her to feel this way about you, while you seem to be a lot less committed.
You have come between her husband, her children, and herself, even at the engagement stage; this is not allowed in Islam. Of course you cannot ‘receive’ her, and even if you could nothing that you could offer her gives you the right to separate a family. As such, you need to walk away from the situation, without explanation, and allow this wife, and mother to return to her senses, and her family. Whatever the consequences of her own actions, this is for her to face. If this means you moving elsewhere, or finding a job elsewhere so that you will be completely out of her life, and the life of her family, so be it!
For further guidance, please try the following link(s):
Love in the Hereafter
Love is Selfless Not Selfish
The Songs of Mustafa Kamal
Good Marriage But Couldn't Resist