I've been lurking on this thread but I had to respond to this:
"i think be honest with them - tell them that sadly you found out he has a girlfriend and marriage means you promise not to have any other girlfriends." absolutely not!
these are very young children iirc, whatever happens between the two of you it is not down to either party to paint the other in a bad light in front of the children, regardless of your personal feelings on what he has done.
I also disagree with those who are saying that the op should refuse to allow her h to see the children on the basis of what he has done. This is starting to border on using the children as weapons and it's not on.
Op - I realise that this has all been a huge shock for you, and I realise that your stance on saying that it's irretrieveablly (sp?) over is firm. But you do need to sit down and talk before you sit the children down and telll them anything. Shutting yourself away and denying any kind of rl support is not the answer, and tbh neither is coming here where people will fuel your anger and validate your decision to keep him away from his children. Yes he is a shit for having had an affair, but he's not a monster or a child abuser, by not allowing access to his children you are complicit in making his children pay the price for this, and they are innocent in all of this. Start playing games now and it will only create a worse atmosphere for them in the future.
By suggesting she take the children over to her house his sister isn't taking sides she is being reasonable.
In an ideal world it would be lovely too think you can lock yourself in a bubble until you are ready to deall with this, but this is the real world and there are children involved here.
You need to stop having conversations ty text and through third parties and actually sit down in a room and have a conversation about all this. Even if your relationship is over you are still bound for life by the children you have together and this at least needs to be resolved. You do not have the monoplolyon when your children should be allowed back into their father's life based on what he has done to you.
Sorry to be blunt, but IMO a lot of what s said on these boards is dangerous and adamaging and enabling of a culture where women are condoned for using children as weapons in their disputes with their ex's.