The chance of winning her back that way (with all the consequences and further repeat risks down the line) has to be weighted against the consequences of entirely alienating her (which likely involves a break in the family and trauma for the children).
Since you are discussing your private life in public, would you mind if I'd ask why would you want to "win" her back? Seriously, she attempted to bring another man in your house.
And if you just dumped her, what would she have gained by becoming hostile?
Why would you want to "win" her back?
Because I was heavily in love with her? Because it could conceivably have been better for child children? Because I could see my failures in it?
what would she have gained by becoming hostile?
That is a question asking rationality from someone not known to follow such a course in an emotional situation...
This is the second post about Dealing with a Major Personal Crisis. The recount of the crisis is complete now. Please continue reading there but comment here.
The reasons for posting it this way are explained at the end of the link. I hope this approach does what I want it to.