Lost One,
I think that you know just about everything that I am posting below. I offer it as a concise review of the history and current status of your situation. Then, I offer some indicated actions that spring from that foundation. If I have gotten anything wrong, I apologize. Please take what is helpful, and leave the rest.
"Douche Bag", or DB, has been in your WW's life for most of her entire life, not just the last 18 months. She keeps him in her life. She loves him. Both she and DB are serial cheaters.
He is her priority, the Alpha. DB is her lover. You are the "good guy" - the Beta: the good husband, father, and provider. She can not let him go because she wants him in her life for "the thrill, the rush, and the attention she wants." She has always picked him and his feelings over you and yours. She withheld sex from you because she did not want to betray him. She deliberately put your health in danger.
She "broke up" with him face to face, not because she wanted to let him down easy. Probably, she wanted to discuss about how they need to cool it for now, or take it underground, until she can settle things down with you, and get you back into place and under control. Even if I am wrong about the conscious act, it may well have been in the back of her mind. In any event, she wanted to be able to leave him with some hope/chance that she would be back, that they were lovers but that the situation prevented them from being together. She is probably manipulating both of you. She is trying to protect her source of stability and financial support. I even doubt she is thinking much about the kids. I propose that you are simply being strung along. She certainly does not act like she is trying to save her marriage to the love of her life. She cries for herself, for regret, and not for you or remorse. She fed you total bullshit with the list of pre-conditions for which you must provide guarantees before she would cut it off with DB.
She is not "too weak" to end it with DB. She just does not want to. She doesn't want a divorce. She does not want to lose her financial support and stability. She may even want a father that is around for her kids. I'll bet that if you were to offer an open marriage, she would gladly continue her relationship with DB and you. In that way, she could have both of you. After all, that is what she has(?) been doing. The possible stumbling block for that is that DB now does not seem to want to share. That is quite ironic.
She cries because she is threatened with losing her cake by your demand that she choose. She is not "torn between two lovers." She is torn between her lover and her provider. She even told you that you are her social security plan for her old age. You heard it differently as a more romantic message.
I would be very suspect that your wife could ever cut if off with DB. Do you want that sword hanging over your head for the rest of your life? Unless she can provide overwhelming evidence that she has discarded him from her heart/mind FOREVER, you should maintain a straight and narrow path to D. She can go to IC for help, but MC is a waste of time while she still has positive feelings for DB. She is the problem with the marriage.
If you want to have any chance at R, and not just a false R, you should be all no-nonsense with her. She should not go anywhere without your knowledge and she should be able to convince you that she is only going/doing that which she has told you she was. She has destroyed every bit of trust that you have in her. If she ever wants trust, she must build it ounce by ounce over a long period of time. She must clearly show you that YOU are her Number 1 priority (perhaps tied in some areas with the kids) in every aspect. If she can't, then she does not deserve your love or support.
Please follow through on the separation, especially financial, to prevent her cake-eating. How she deals with your withdrawal of finanical support from her (not from your children) will be telling. She may show you that without providing the beta support, you do not have a roll in her life. On the other hand, she possibly could disprove my cynical assessment.
If you have any doubts about her being truthful and forthright about any critical facts, do not let her stonewall you on the polygraph. If she has disclosed everything truthfully, she will have nothing to hide/fear. She should be willing to provide you with this means of assuring you (thus providing much needed peace of mind) that you actually know with what you are dealing.
The path to R or D is not linear. Threads on this site are continuously proving that fact. It will be a difficult, long process. You need to make sure that you are not setting yourself up for only continued disrespect, low prioritization, and disappointment. She has to provide some concrete, believable reason for you to start pushing that immense boulder every day to the top of the reconciliation hill. You do not want to suffer like Sisyphus.
Her demands for the "lists" were, IMHO, a stalling/deflecting tactic to slow thinks down until she could convince you to rug-sweep her affair. Then she could pick back up with DB (along with taking it deeper underground). The "only one list away" statement was as egregiously deceitful as could be, with the sole purpose of guilting you into submission.
Consider taking this particular take, adjusted for what you know that I have not gotten right, on your situation as a working hypothesis. Act on it as though it is totally correct. Blend it with your 180 process. As time passes, conditions change, and new information emerges, adjust the hypothesis to keep you on target for the outcome that you want.
Sending strength and support.
This is probably as close to a PERFECT explanation that anyone could write. I hope you read it a few times.
You also need to start searching for a "burner phone" EVERYWHERE she would never expect you to look. Her car, lingerie drawer, suitcases, etc.
You stated that she could sneak off even if the casino is cut off. ABSOLUTELY TRUE since you said she works from home while you are gone.
Now add in she refuses to even answer when you ask has she contacted him again. Do you want to spend the next years wondering where she is every time she walks out the door.
Lost one, you do NOT have the information you need to make any decision based on facts.