I'm sick of my brother living in my house. I'm ready to destroy my wife's relationship with him to get him out
Why are you feeling so angry towards your brother?
He is using all our money on his games and he doesn't even thank me for the food I bought. His face also looks like shit because of the internet addiction.
Having family stay with you is a nice gesture for awhile, but he has over stayed his welcome. Why not just ask him to leave? Destroying a relationship to get him out is quite a negative move, they will be hating each other for your personal reasons.
I don't really want to deal with him at all and I would rather just ignore that he's around and take my wife out somewhere nice.
It makes sense that you feel taken advantage of when you are providing all of this to your brother. Be careful to not enable him in this situation as this could actually be doing more harm than good to him. You are better off focusing on making your wife happy anyway.