Dad dating 4 mo after mom died

So, the situation is a little complicated... My mom suffered from depression for many years, and it sunk into severe depression this last year, and in October, she took her life by jumping off the roof. I was living abroad at the time and came home in order to help out at home. It's now been four months, and while I've been doing well with handling everything, what I'm not able to handle is my dad. I acknowledge that he's been grieving in his own way, and because of this have been very patient with him, but he's pushed me to my breaking point. The past four months I have had to deal with him being very short tempered with me, obviously taking his stress out on me while restraining it for everyone else. This involves him cursing me out, yelling at me, and suddenly sweeping everything off tables. Not a single time have I raised my voice at him. He has been very poor at communication, asking me last minute to ask help with tasks when I have my own job/life to manage. Since I came home with the goal of helping the family, I put my life on hold and do what I can, but I can only do so much when he gives me such little warning. But that would all be tolerable, if this latest thing hasn't happened. So my dad started dating about a month after my mom took her life. He never told me. I had to find out over Facebook. Last week, I came home from work and there was a woman with him in the house. He introduced her as his "good friend" Well, two nights ago, I woke up to them having very loud sex. So not only did he bring her home to our FAMILY house, where I have two teenage brothers AND my grandma who live with us, so all of us had to hear, but he never even told us he had a girlfriend. Because they were so loud, i couldn't sleep, and went downstairs to sleep on the couch. The next morning he asked me why I was on the couch and I simply replied, "Your walls are very thin." He instantly got defensive, and complained about just wanting to "have a life" and "have some privacy" and then tried to accuse me of sneaking around with a guy (which I haven't) in order to justify him sneaking around with this woman. Luckily, I had planned on moving out yesterday, so I didn't have to deal with it, but I had to come back home today for work, and she is here at the house again. He obviously doesn't understand how much it hurts to see him with another woman, nor apparently the common courtesy of having loud sex in the family home. I would appreciate some insight into this situation/how I should approach it. Thanks.

You said, "My mom suffered from depression for many years, and it sunk into severe depression this last year, and in October, she took her life by jumping off the roof." Was your mother helped with her depression? Was she getting any treatment? Was she taking any anti-depressants?