Re: Did I make a mistake breaking up with him?
There's a lot of information in your post but two things stand out to me:
1) Why was your Mom such a mess over not being invited? Did she know you'd invited your Dad? I'd understand if this was a "special" birthday or if she'd not been invited to a party but dinner for 24? I see no problem with her initiating something like asking the two of you to come over that evening or the next day for cake and ice cream. But to have a crying fit over not going to dinner with her daughter and boyfriend seems very manipulative to me, especially if she was trying to intercede on a possible re-connect between you and your Dad.
2) Why couldn't the two of you have gone out, then gone a second time later? With 3+ hours between meals, it seems you could have done both and maybe just split an appetizer at the second meal. Did your Mom even need to know there'd been a first meal with just the boyfriend? My point with this is that sometimes big blow ups are about small issues. I mean isn't this really a pretty small thing?
Are you able to talk when things are calm or does it lead to a fight?
It absolutely is not right for your boyfriend to yell at your and make you feel bad about yourself. How does he see this? Does he think he's in the right when he does it? Any chance he understands he has a problem and is willing to work on changing. Because if he doesn't think it's a problem, it's not going to change. You should not have to plan on spending a life being verbally beat down because you fell in love with someone who likes to yell you down. But if he really doesn't like himself when he's doing it, and he would like to change, then there's hope.