We sometimes physically fight, but want to be together

My fiance and I of 8 years recently got into another physical fight a couple months ago. This wasn't the worst one, he shoved me and squeezed my face really hard, telling me he would show me what a bitch is after I called him that several times. We do not know how to constructively argue; there is always a lot of name calling and bringing up the past and yelling. Sometimes we physically fight. Sometimes he's started it and sometimes I have started it. This time I called the cops and he was arrested. I am currently living with my parents and he is living in our apartment. We both want to work on the relationship and have started seeing a counselor separately and have said that if we get back together we will start couples' counseling right away as well. We both want to change and be together again, but I'm not sure what to do. I want to be with him again, but my parents hate him and never want me with him again. I am ashamed that I let it get like this and feel like a failure for living with my parents again and no longer on my path of marriage and eventually having a family. We were each other's best friends and confidants and I have no idea how to cope with at least taking a break and possibly moving on. We've both invested so much time and energy into this relationship; neither one of us want to quit. We want to fix it, but I am not sure if it can be fixed...