Pressure for dad to walk me down the isle

Hiya
So my relationship with my dad has always been strained. He has an alcohol problem and can be really difficult and childish. Some of the things he said and did when I was growing up I've found unforgivable. There was a period in my twenties when we didn't speak after I caught him telling my mum awful, and untrue, things about me. Things are much better between us now, but he still has this nack for making everything about himself. I've been through therapy a few times trying to resolve issues around it.

I don't want anyone to walk me down the isle. The whole thing gives me the absolute ick, regardless of my relationship with my dad. I've told my mum and dad this, and agreed that my dad can walk me to the church door, but no further.
This has apparently caused such a lot of drama at home. My dad has been saying it's a public humiliation, and acting like I'm using the wedding to punish him. He didn't go to the suit fittings, because he'd worked himself up so much that he had a migraine. Mum's been putting pressure on me to let him do it because his behaviour has gotten so much better very recently - which it seems they have. I'd probably be willing to set aside my feelings and let him do it if it wasn't for how things have been in the past.
I'm on the edge of just giving in because I'm worried he's going to cause a scene or make himself conspicuously absent on the day. It's really upsetting me, and the whole thought of him walking me down the isle makes me feel so uncomfortable but I can just see him making it incredibly difficult if I don't let him.