I would also not invite him.If he’s the type that would usually cause a scene, I’d say don’t invite him at all, but that’s just my opinion. Go with your gut, it’s your day and the only people who should be the focus is you and your future husband. I didn’t have any family at my wedding and eloped, because I knew in my gut that certain people would ruin it and take over as they always do. Do what makes you happy
My dad completely ruined my wedding for me. He made a big song and dance about how he wasn't going to come, sent horrible emails to me in the weeks leading up to it and after every email came a deposit into my bank account (controls with money, which i don't want or need). Long story short he did turn up on the day but my head was spinning anyway so I ended up basically ignoring him and mainly crying in the toilets. Afterwards the emails resumed, he thought I was ungrateful after all he had 'paid his admission fee' and I treated him poorly!
People will say oh it was such a lovely day and blah blah but honestly it was just about the worst day of my life because of my dad.
I think in your situation you need to understand that he may go out of his way to ruin the day for you, whether he's invited or not. That was certainly the case with me and every day I wish I hadn't invited him.