A little story for you...
...actually, no. No story. It's a long 'un, and I don't feel like telling it right now. But suffice to say, I had a breakup so spectacularly, cringingly awful that bards will sing of it for centuries to come - and then met a girl who made me happier than the one I just broke up with, the one I was engaged to and had been with for nearly five years.
In doing so, I quickly found out several things:
1. Self-respect is damn important, and it's something that you can easily run out of.
2. Joy, on the other hand, is infinite. There's no upper limit to how happy you can be. It may seem that way - in fact, for the five years I was dating that godawful cow I believed myself to be the happiest I've ever been or ever could be - but every now and then something will make you even happier, forcing you to redefine happiness and what it means to you.
In short, mate, every time you think you're the happiest you can possibly be,
you're wrong. You WILL be happier.
I say dump her as quickly as possible, and ensure your boss learns that this sort of behaviour is not acceptable (use whatever methods seem fair to you). If you still feel resentment towards your boss, console yourself with the fact that he'll always feel a little bit edgy about whether or not she's cheating on him - after all, she's done it before, so there's nowt to stop her doing it again.
Cut it clean and move on. Don't try to stay friends - if in a year or two you meet up and you can put it all behind you, then go for it, but don't try it right now - and then get on with your life. Right now she's simply a drain on your life, and you're spending far too much time being panicky and miserable.
*DISCLAIMER* - as you've probably figured out by now, I've been in your situation - as such, I am in NO position to offer an objective viewpoint on this topic, so take my advice with a pinch of salt.