Should I kick my 17 year old son out for good? Advice please!!?

Came home early last week from work and found my girlfriend of three months half dressed (40) and my son (17) all cuddled up on my damn couch together. I started yelling and she ran out. I was so mad that I told him not to say a word to me, because I knew if he said anything stupid to me that I was going to probably back hand him, and I don’t believe in hitting my kid. I told him to get a bag packed and I called his mom and took his keys and dropped him off to her. It was probably about two hours after I dropped him off that he started calling my phone crying pretty badly. I found out later that his mom laid a belt whipping on his behind for his actions. He just kept on saying that he was sorry and he wanted to come back home. Sadly, I didn’t even feel sorry for him. And as for that b**** of women. I tried to call the cops to press charges against her, but they said that at age 17 he was legal age to consent. Which is total bull to me, at 17 I still have to tell him to do his homework and to make his damn bed, legal age…crap! (Also his mom saw this woman on the street and beat the crap out of her…my ex-wife is crazy.)Anyways, now I have the decide if I’m going to let him back in my house or make him move to his mom’s were I know that are going to be a hell of a lot harder on his a** than I am. I mean I have worked hard to move him to an upscale neighborhood, private school, he doesn’t have to work, I bought him a new car, and anything he asks me for I get him. I have never wanted him to be label white trash like I was when I was younger. I’m just crushed right now… I just can’t believe he did this to me! Any advice?