Okay, after it was obvious that you weren't going to do it and kind of stopped talking to her, did she apologize and say something like, "Oh forget it. I'm sorry I made you uncomfortable. Let's just go back to the way things were"? Or did she keep bothering you about having sex?
Regardless, you have to ask yourself if the sex is one time or a regular thing. Is she seeking a way out of her marriage? Does she want you to be a step-dad? If it's a regular thing than it's a relationship no matter what, however illicit. This is extreme drama no matter how secret it is. Two relationships are being disrupted - her and her husband (and kids!) and you and your girlfriend. No one involved is abusive or "deserving" of such cheating so it's all-around kind of unwarranted drama, know what I mean? You're not choosing to have this relationship with her out of extreme sympathy for her because of her abusive situation or the fact that she's almost homeless or whatever. It's just some sexual pleasure that she's seeking.
You have to wonder. A man's sex drive is VERY often stronger than a woman's, right? Why would her husband not want to have sex with her? Why would he be so unhappy and dissatisfied with her that he would choose not to get it on with his wife?
I don't think you really want the complications that this will bring. You'll feel guilty and everyone will probably find out, and then all hell will break loose.