Didn't want to spoil the love-in last night and appear on the thread, as a humourless Mrs. Stern... 
However, I wanted to reiterate that I never did advise that you asked questions of your H about the affair Solost. In fact, when you once suggested it, I recall that I recoiled in horror at the very suggestion. What I actually wanted you to do was to have some understanding of the affair yourself, because I do think that's important to your recovery and also for any future relationships. It was why I gave you an alternative affair script, that placed the responsibility firmly on to him and not you or the OW.
That said, when you didn't follow that advice, I wanted to say that I understood why you felt you had to ask him. I don't think that approach was helpful to you though, because unfortunately I think it set you back into believing his script, which as you know, I think is a pack of lies.
My strongest advice is that you never ask him for details about the affair again, because he will lie and you will believe him. Plus, it is much better that he thinks you don't care any longer.
I do think you need to rewrite your script though, because it still casts him as an honourable man with scruples. That won't help with your detachment.
I do hope you think about seeing him less and for his contact arrangements with the DCs to be separate and away from the house. Regarding the DCs questions about the change of venue, it is perfectly normal for the non-resident parent to see children on neutral territory.
Your situation is the abnormal one and is I suspect, causing confusion for the DCs, especially when they see him continuing to treat the house as his home. I think this adds to their belief that he might come back home, but like I said before, I wouldn't assume that this would be what they all wanted at all and they won't necessarily all feel the same. It's just as possible that one or more of them is worrying that he might come back. And that's as damaging as false hope.
It sounds as though you are doing well this week though, with the detachment.