Should I ask my husband to leave or not?

I have been with my husband for 6.5 years and we have been married for almost 2. I met him when I was 16 and he was 21. He was recently separated from his ex wife who he had been with for 6 years and There relationship ended because she cheated. our relationship started out as a sexual one. At the time he lived 200 miles away and we only saw each other on weekends. when I turned 18 I moved in with him. We lived together for a little over a year and had a few problems that stemmed from his lying to me about silly things that wouldn't have mattered if he had just been honest with me about them in the beginning. He ended up cheating on me twice within a matter of a few months and I was devastated. at the time I couldn't imagine my life without him and I agreed to try and work things out. He had always had a drinking problem and agreed to quit. He did okay for about a month and started drinking on occasion and it progressively got worse over time. This whole cycle has gone on since then. on top of that, he has never trusted me, even though I have never done anything to deservethe distrust. I was very understanding about it for the first few years given what had happened with his ex wife but I lost that understanding when he cheated on me and the fact that he asks me every single day if i'm cheating is completely wearing on me. I have always been 100% honest with him. for the last year or so, I've been finding myself questioning whether or not I did the right thing trying to work on things with him. He still drinks on a daily basis and I no longer enjoy sex with him the way I used to. Most of the time he's drunk and I don't feel that emotional connection with him in that state. I don't know what to do, I still love him but I don't know if I love him enough. I get really frustrated and irritated with him on a daily basis because of the drinking and accusations. If I miss a phone call from him he automatically assumes I am cheating. It drives me crazy. What do I do????