It seems like you went through a lot of stuff very quickly. It seems like it's the first time you've gone through this but believe me, it gets better with time.
I don't know if it's even worth for me to post my two cents at this point but I just hope you can benefit from the wisdom of my experience.
After what you said that she was hesitant to break up with him even DURING Christmas break, I'm not really surprised at all that she decided to stay with her boyfriend. It seems like she's created a very hurtful dependance on the guy considering he has been with her for three years. What We KNOW she's cheated on him. (Does the bf/Jordan know that?) Usually when something like that happens there is a terrible rift in the relationship. My take is that eventually they WILL break up. She just needs to grow out of that dependance on him.
But enough of her.
I think the first few times are terrible and heart breaking but with time rejection isn't more than an "oh well, on to the next girl" if she doesn't accept you, IT'S NOT YOU AT ALL!! She's just not the one!! Sooner or later, someone WILL come along who will make you happy and trust me the wait makes your end in sight so much more worth it when it finally comes along.
When you're young (I'm still 20 but I have an idea of how it is,I was once very dependant on a relationship about two years ago) you create a sort of fixation on a person and you somehow convince yourself that there is absolutely nobody else and how could you ever go on? Believe me. Life goes on. Hearts are really broken every day. It's tough when it feels like the whole world is ending to accept that it happens all the time.
As far as your relationship with her goes, right now, sorry to say, it's done. You won't be able to be friends with her without wanting to have her in a different way. You might be able to hide but your hopes will always be right there. The rest of the people in this forum are right, split, man. It'll be oooh so difficult to not have your drug (the girl) for one day but every minute that goes by is easier than the last one ...well, maybe every MONTH that goes by.
There are millions of women in the world, man, get out there and have fun. Find another Kate. Find someone else and be happy.
I've found that life is a bitch in this case, though. When you're waiting for the one she'll HIDE if she has to. When you're casual and cool with yourself and content and confident with you being single, they'll flock for you. Basically, women sense desperation on a guy like the plague ...and they'll act accordingly. Not good.
So be cool, go out with your friends and have the best time you can. Ms. Right will show up in due time. Best of luck.