Read the thread, good to hear Sunday was positive after Saturday night, but it's going to be a long job as people have said. Ups and downs.
I know a lot of folks have said 'don't worry about the kids, they're adults, they can cope' etc. But I'm going to chuck in my tuppence. It sounds like you are all still close, for their benefit, keep them in the loop and treat them like the adults that they are. Don't be tempted to lie and sugar coat things for them. I was 18 when my folks divorced after 23 years and the initial foray took 3 days from announcement to empty house. Do not underestimate what a shock to the system that can be for them too. Yeah, you need to look after number 1, but don't just presume it's not going to hit them. The life that they took for granted for 20 years has just radically changed. The stability that they expected isn't there any more and potentially what they presumed was a functioning marriage has turned out to be a lie. If you felt they'd believe that your wife was 'sleeping in another room because she had a cold' then this whole thing is going to have come out of the blue. There's no reason one or both of them aren't going to be going through something surprisingly similar to what you are going through.
I don't know the specifics, none of us should, and all of this advice is worth exactly what you've paid for it. It's life experience not real trained knowledge or anything. But hopefully one of us will say something that helps, even by accident. Hopefully you and your sons can be there for each other in this.
It sounds like things are going in the right direction, I hope things turn out as well as they can.