Brutally honest?
She seems like the worst kind of example of our sex. The lying, cheating, manipulative, using, selfish female who has had many of my male friends asking me why they bother. I am, at best, what my man call bi-curious, but I guess some naive part of me thought that women would treat each other better than SOME, NOT ALL, men treat us, and better than we sometimes treat them.
I think she has been consistently testing you to see how much she can get away with, and she's learned the answer is, "a lot." She may have a real addiction to online sex, but that only gets fixed with a lot of work on her part, and a real desire to change, just like quitting smoking. I don't see any evidence of her wanting to change. You say she is a student, implying she is broke, but then she can BUY a house? Maybe you just skimmed that, but where did that money come from? Anyway, even a broke student can use student health on campus, and they will help with mental and physical health issues, including addictions, and Sex Anonymous (or whatever it's called) is free, just like AA, last time I checked. Yeah, chip in a buck or two for coffee, if you can, but no dues or meeting fees.
I'm sorry if I sound harsh, but, even if you are an axe murderer, you deserve better treatment than this. Do not give up your babies for her (yes, I have animal issues, too, but then, I can credit one of them with saving my life in a roundabout way.) Don't give up the home that means so much to you. Give her up, spend some time healing the hurt she has caused, then decide if and when you want it to look for someone who will value you as you deserve.
Best of luck to you, and please, let us/me know how you are doing-you can PM me if you prefer.