Boyfriend issues/Family Issues

So my baby's father and I have been together on and off for 2 years now we've been through so much, honestly! Like an abusive relationship and so on. I'm the beginning it was all so great but once we moved in together, things changed. He got so "overprotective" as he calls it. We've been to the point where we throw punches at eachother when we fight. This usually only happens when he's drunk. As time went by I noticed he had a drinking problem and as he stopped drinking things started to get better... he's genuinely a nice person and cares so much about our babygirl. It's been 3 months since we haven't "fought" or been in a serious argument but all my family hates him and thinks that he's never going to change that it's an act.. I honestly don't know what exactly to believe or what to do? Should I leave should I stay.. he asked me to marry him, I do love him. But I have no idea on what to do especially because of our families.