My friend, I feel for you. I felt uneasy just reading your story... I know a stranger's 'sorry' won't make you feel better or make this whole problem go away, but you came here for a reason, vent it out, see what people think, etc.. So here is what I think:
I usually promote communication, and problem-solving together, counselling, or just trying to work through any issue that could make people drift apart.. I could ask you for details, what you did or didn't do to make "us time" slip away, or what her role was in the relationship struggling, if you guys tried working on it over the years or not... But not this time. Not when the betrayal has already happened.
If I were you, I would just leave. She spent the weekend, and she admitted to a kiss. I may be negative, but as soon as she mentioned "fantasy" I thought to myself, sure, you kissed in a moment of crazy passion, and then you each went to your separate bedrooms and fell asleep over a boing book... Ok, I am not being nice, I do not know, nor do you.. But it doesn't even matter, even if it was just a kiss, I could never look at my wife the same way...
Obviously, as parents, kids need to be a priority. (And I do not mean staying together for them, speaking as a child of divorced parents, trust me - staying together does no favours for them). By that I mean that I would separate in the most calm and humane way possible, no need for the children to witness fights, arguments, name-calling, or any nasty stuff. I would just say that it betrayed my trust, and regardless of me still having feelings and loving her, it is not something that could ever be undone.
Ultimately nobody can tell you what to do... I just really wanted to let you know that I symphathise, and shared how I would react.