The first thing I would do is GET A LAWER!
SHE has gotta move out.....as much as you love her...SHE can't stay....she CHEATED on you! Obviously she does not have the same feelings for you as you do for her....forget the explanation from her...that will come later...maybe.She knows what she has done is wrong.... Just be a man, pack her stuff and tell her she has to go. Don't talk to her about it...just do it.
Why would you leave? You did nothing wrong. She is the one that obviously does not want to be in the relationship...let her go live with her "boyfriend" or parents...whatever...not your problem! She will not have alot of sympathy from friends and family as she is the one who cheated...not you. You need to show her the consiquences to her actions...and you leaving the house will almost be like a reward to her.(she cheats on you and she gets to stay in the home that you work 4 jobs to try to maintain....while you go live in a motel!!!!) I don't think so!!
There could be 100 reasons why she cheated. I am no expert, but I have had experience with this kind of thing,(divorced with 2 kids), and it could be that you were working too much and she strayed...it could be that she just strayed "because"! There are two sides to every story...and somewhere inbetween you will find the truth.
Whatever the case may be, this is the hand you have been dealt. You need to do what is best for YOU, and her staying in that house will do nothing but eat you up inside.
You need to get legal advise to protect yourself. You have time and $$ invested into this relationship. All of which is 1/2 yours and 1/2 hers. If she has screwed you by cheating on you, she may take it further by trying to screw you financially.
There are plenty of women out there.....hate to sound shallow...but one of the best ways to forget is to be with others.
Just be glad that you don't have kids with her....at least I don't remember reading that you did....That makes things a WHOLE lot more complicated.
Get a lawer
DONT destroy any of her stuff
Get her out
Don't be rude to her....this will just bite you in the *** later...just don't talk to her.
It seems really brutal right now....but it WILL get better. You need to focus on what is best for YOU.