I'm so sorry you are going through this pain. But NOP is right, cheaters lie. The problem in your M has never been about OM, so I am not sure why you are letting that make or break things.
You are wrong that your W has made no effort or given you nothing. Her emails and discussion tell you that she is open to working on things. What she has not given you is what YOU want on YOUR timetable. W is all over the place. At one moment she probably feels that she needs to try everything to save her M, at another moment she probably sees it as pointless, and counseling as something that she will only do for the sake of the kids. She doesn't know what she wants, though you are really pushing her to make a decision before she is ready. And, that will surely be a decision in favor of throwing in the towel. You have to give her time and space to want to try to reconcile. Even if you have no interest in reconciling and you are going to S and D without doubt, then there is no reason not to give her the time and space, for her private life is then no longer your concern.
Please quit sharing with your kids. It is enough for them to know that Mom and Dad are having some problems. Period. They don't need to know what they are. You don't need to bash Mom. It is VERY damaging to put them in the position of having to bash Mom to avoid feeling like they are betraying you.
If you are set on S or D, then I really don't see how it is any of YOUR business to tell HER parents what is going on. Don't lie, but don't involve yourself unnecessarily. If contact becomes necessary for some reason, simply tell them: W and I are S. There is no productive reason for you to get into more than that with them.
That being said, take care of yourself businesswise. Let her pay her Visa. Can you sell the BMW to limit your losses? It doesn't make sense to give her an expensive piece of property like that on which you are still making payments.
Keep enforcing your boundaries — you said no calls, she made them, stop paying her cell phone. Block his number from the home phone. But don't do it with drama, just do it. "W, you have not respected my no contact boundary. I am taking steps to enforce that boundary."
I really do not think you are anywhere near emotionally ready for a D. When you are ready to D, it is no longer that big a deal in many ways. Right now, you are very emotional and acting out. Your pain is raw and deep and jagged. It simply doesn't feel like that when you are ready to D. Again, if you haven't, for your own sake and your kids, read DR. Read some sitches like GH's. You are losing the advantage you started with. If you decide to DB and participate on one of the DB forums and would like me to check on you from time to time, let me know.