@amaninlimbo,
If you loved her with all of your body and soul, etc., you'd end your marriage.
Is she working on her marriage? Possibly. What did she mean by the last thing she texted? We have no idea; you know her better than we do.
In the meantime, you are teaching your children that love doesn't matter and that it's okay to stick around when you're treated like crap. Not such nice lessons, eh? Your kids know there is something going on. Only the extremely young (infants) or challenged or oblivious don't. Operate under the assumption that they know or can guess or at least realize there is something happening that is out of kilter.
Want to do right by your children? Then either work on your marriage (suggest counseling to your wife and, if she won't go, then go alone and at least get tools to cope with staying, or with leaving) or get outta Dodge. Affair limbo is terrible for everyone, and your children, once they really put it all together, aren't going to want to hear about your sex life with your wife. They'll be hurt and angry and will feel betrayed.
Do this regardless of whatever is going on with your affair partner. She is not part of this equation. Stay and make a go of it, or leave. This in-between bullshit is for the birds.