No bullshit... Do you love this woman?
If you love this woman and this woman loves you, then you make it work.
The first thing you do is no more "Talking about splitting".
Don't get pissed and say, "Well, I'll leave", or "why are we together", or any of those "splitting up" type of statements... They do not do anything but drive a wedge.
As far as the fucking thing is concerned, you weren't together, it's done, she probably fucked people before you, so you shouldn't let the general premise of her having a dude between her legs be some big deal.
Hell, you'd probably have gotten some ass in there if you could, right?
Just move on... talk to each other... Be honest.
If it's meant to be, and you guys love each other it will work out.
If not, then it won't and you can go back to banging hot young vag on the reg.