Most Helpful Girl
Ok, breaking up would probably be the best move for you at this point... but actually break up with her... don't just cut off contact, that is the most chicken shit thing one person can do to another person, say it's not working or whatever, but tell her! It is more hurtful if you just disappear than if you just say hey this isn't working. That's all you need to say, and you will be a better man for it.
Also, I personally wouldn't track down her boyfriend, let them work it out. That is THEIR relationship and it's not your job to manage that.
Most Helpful Guy
The new Skype idea sounds plausible , but I don't know about looking her BF up and stirring the pot. I agree what she is doing is wrong ( if she indeed does have a guy there ) it is the middle of the night there , just send her an off line message saying your goodbyes and don't be on the Skype page anymore. If that is a senario you can play out and be good with then go for it