False Rape reporting? *Long post*

My dad is an alcoholic and acts beyond crazy. He fought for my boyfriend to be able to start spending nights here ever since we hit 7 months, but then backtracks and gets mad that he stays. My mom is completely okay w my bf as he helps out. The last time we argued about my boyfriend staying (at the time he had stayed a week bc he got a week off work) he admitted to being a control freak and “promised” he’d butt out of my relationship. Well my boyfriend ended up losing his job and has been struggling w mental health, he’s been staying here for about 2 weeks now bc his family isn’t as sympathetic to mental health like mine is, so they’re harsh about it. This morning, my mom told me he brought it up to her and was mad, which upset me bc he’s been fake to me about everything. So she thought it would help to get us to talk it out - bad idea. He said he thinks I “lost my focus” (which isn’t true, I still work and do everything I need) and when I tried to explain it, he cut me off and got in my face, yelling. I ended up yelling at him to leave me alone bc he wouldn’t listen and I tried to walk off, to which he chased me around until I was able to get to my mom, who hugged me and told him to knock it off. He got mad and said that to make him leave he would just call the cops for rape, threatened to sell the house from under us, talked shit to my mom, threatened to kill himself, and than ran off to a hotel. It doesn’t seem he’s coming back anytime soon but idk how to move on from this. I’m so hurt my dad would betray me like this. Any piece of advice?