Initially it didn't work, then he wanted to reconcile but he couldn't leave her (since she had moved in and is still living with him)
Couldn't leave her? Or wouldn't.
He is making choices, just as you did in the beginning of your marriage by not telling your family and not living with him.
She is quite crazy ( i cannot ring him or text him in front of her) as she loses the plot.
I am not sure why you think she is crazy. Sounds to me like she's protecting their relationship. And your H is allowing this. He is not "helpless" in this situation.
What do you think he told her about you? That you and he were married, but you refused to tell your family, and refused to leave your family home and live with your husband. The truth. I am not judging the truth, but I'd like you to put yourself in her shoes - your H explained the situation to her, and apparently she fell in love with him. "Oh poor thing," she thought, "his wife wouldn't leave her family, what kind of a marriage is that? I love him even more for the indignities he's had to suffer...."
I guess what I would do in your situation is to tell him that you love him, that you don't want to give up on your marriage and you see the error of your ways - that you want to live with him as true husband and wife, the way it should be. That he is having an affair which is obviously a bad idea for your marriage - insert religious or cultural reasons if that might help, i.e. living in sin, etc. Start a strong Plan A - fulfilling his needs as best you are able to, telling him that you're showing him how good it can be when he chooses to give up the girlfriend and work on your marriage. Tell him that you are very sorry for not honoring your marriage and realize your mistakes, and that you will be the wife he imagined. And tell him that you are very unhappy he is having an affair and that you certainly hope he ends it. Then decide for yourself how long you are willing to tolerate his infidelity, and if that mark passes, go to Plan B.