My relationship is getting way tougher since we moved together

Gee you're right. Relationships get tougher when you're living together. I moved in with my ex too soon back then, I mean I feel like now I need to know people SOOOO much more before I would move in with them, unless I want a recipe for disaster. But you learn about people so quickly that way. But living together is a bit like marriage, I can understand why the sex goes down a bit, because now that you can get it 'anytime', actually you don't want it (or she doesnt). Its just some psychological effect. Plus the arguing and fighting makes it less likely she wants to be intimidate when she's mad at you. I think you really need a big talk and look into splitting up or at least someone going away for a while so that you both can think about what it would be like if you weren't living together, whether better or worse.

Moving in together is a huge step. You can totally expect her to lounge around looking like crap, for your sex life to slow down and for you both to start nit-picking about stupid crap.

That said, you should also grow closer, more comfortable together and fall deeper in love. If you aren't getting the good with the bad, then it's a good thing you moved in together before you locked into this by getting married!

Kick her out!

These look like the first signs of a problem in a relationship. It all starts like this and if you don't do something now, you might end up going on different ways. At times, even if you do something that still happens but you can say you at least have tried.
Talk to her up front. Tell her that you feel some things have changed and how you feel about them. The key in such talks is that you shouldn't be inquisitive, judgemental or defensive. All you have to do is to control the energy of your voice. She would be more willing to talk about things, even if they might be hurtful. Though a relationship is the ultimate point you can get on a personal level, don't take the things she says personally. Try to understand her points from her perspective. After all, it could be something you have done that made her give you the cold shoulder. And some things just don't work. Admit those possiblities and accept them upfront and try to be understanding before talking. That should make you a lot more comfortable while talking.