Poor kids anyway. Whichever way they’ll end up ferried between 2 houses. Missing their dad at Christmas etc.
To be honest some of the stuff you say is pretty offensive to families in which parents are no longer together as a couple.
It is perfectly possible to coparent with loads of love and security for the children.
The reason that will be difficult is because your husband won't make the effort, I understand that, but please stop generalising by doing down the idea of parents separating over and over again.
You make out as if people who make the painful and difficult choice to split have done more damage than keeping their children in a home with one totally unengaged parent and both parents modelling an incredibly unhealthy relationship.
People have been trying to help you sharing painful experiences of break ups, their stories of starting a new home with their children etc and you just seem to be determined to reiterate how bad it is for parents to break up.
Being together (despite the damage it's doing to the kids) "fits socially" you say? Keeping up appearances really shouldn't be the priority here.
Good luck, I don't really know what you want but I think it's just to confirm your husband's second affair. Which won't change anything about his parenting. So won't help your kids. So I don't know why it's your priority but it's your prerogative.