For what's worth, I've seen IRL marriages with OW/OM fall apart spectacularly within few years. All because their relationship was built on a house of lies. I wouldn't put too much Vegas chips, nor even the fake ones for that matter, on H and OW's marriage.
Focus on you and your connection with the kids. It'll matter VERY much down the road in short years. And I wonder what S thought of the 'news'...probably threw up in the back of the house if H did ask him to be his best man.
There will be always that primordial connection between the child and the birth mother that will always remain there until death. No worries there. I mean...why give the OW some head space if she's a real piece of work, right?