You actually do have a chance of turning this around but it involves a lot of work and a lot of change on your part.
As for expecting you to pay for the apartment that you can swap, tell her
"NO, I've decided I won't ever be doing anything like that. You cheated, you wanted out of the marriage, well then you need to leave, start looking for a place you can live, get a full-time job and put your university classes on hold and get yourself an apartment where you can also keep the kids half of the time. I don't care how expensive an apartment is, you made these decisions, you deal with those consequences. I don't plan on moving out of my home anytime soon but I would like YOU to leave ASAP, if you need help moving let me know."
You have been way too soft, it's time to stop that.
"What is best for my kids is best for me"
Persevere = happily being patient over a long period of time