The more my fiancee & i love each other the more pain we cause for each other! How can i get her back? Advice?

Im 26 and was with my ex fiancee for 6yrs, engaged for 2 but we broke up 2mnths ago, She is 24 and we have known each other for 20yrs as our parents are friends. My brothers and i have earned ourselves a bad reputation, I want my girl back in my life, But we have a love-hate relationship our love is crazy, we're nuts, When we were together we were so happy and i love her more than i can stand it, Although i loved her so much, I am easily pissed off and have a really bad temper that if we where having a disagreement i would always shout in her face, violent words & smash something against the wall or sometimes even punch the wall/door & if she'd try walk away from me i'd grip her arm & i know i shouldn't have done that, Other times i'd call her a c*nt or speed in the car when she'd beg me to stop, But when we weren't fighting we couldn't of been happier, I always told her how much im in love with her and wanted us to marry & start a family, We'd always have our hands on each other, snuggle and our life was unbelievable. I grew up in a home where violence was the answer to everything, but i would never hurt her intentionally but she knew how to push my ons and i'd always lose the head with her and it would kill me seeing her cry but we always made up and she'd call me a f*cking a*shole among others, even push me, her temper can be as bad as mine but we would laugh about it later. Our friends always said he have a toxic relationship and don't know how we lasted as long as we did. When she broke up with me I dated other girls and she stayed single, every girl i was with couldn't compare to my ex and even when i'd sleep with them i thought about her. I asked her to lunch yesterday and told her i wanted her to take me back and she told me that it's sick that all these battles are what keeps her satisfied, but says things are better as they are now but cant imagine us being apart forever, She is the love of my life, I'm tired of the games & I just want her back. Any advice?