I vote for one more time of laying it on the line, very bluntly and maybe even emotionally (emotion might translate to you being very serious about this, not just being a drama queen).
"Anna, I'm really worried about something, and I need to talk to you. You like to embarrass me. You tell stories about me to other people--repeatedly--that I'd rather forget. You think it's fun. I don't. I get hurt, I get humiliated, I get anxious, and it ruins my day. I've tried to talk to you about it before, but you just tell me to lighten up.
Well, you know what? I don't have to lighten up. It's how I am. And I don't like being repeatedly humiliated by someone who is supposed to be close to me. You may not agree with it or even understand my feelings, but you don't have to. I'm telling you that the stories are not funny to me. You know, you don't like (name of food she doesn't like). How would you feel if someone constantly served you (food), knowing you don't like it, and then belittled you when you wouldn't eat it or got annoyed at him?
I've been thinking a lot about this habit of yours, combined with my wedding, and the thought of you telling stories that you know embarrass me and humiliate me on MY wedding day, to MY wedding guests, on the most important day of my life, is causing me a lot of stress. I have some friends who are telling me to just not invite you if I can't trust you not to try to embarrass me or intentionally try to sabotage my special day. I really don't want to have to do that, but I'll do whatever I have to do to make sure that the only think I'll have to worry about on the most special day of my life will be the weather.
And please don't tell me to 'lighten up'. That's getting old. And really, that old line is just a way of blaming the victim. And this request isn't just for my wedding day, it's from this point forward. So please tell me your thoughts."
Yes, there's a certain amount of snark in there, but I think you need that to make your point.
My story: When I was in college and right after I graduated, I spun out on icy roads at about 55-60 mph, twice within a two-month timespan. For years after that, skidding on snow or ice made me tense at the very least. This went on for years, because, I think, the conditions weren't something that I was exposed to very often. Well, I met my dh, and he would sometimes try to skid a little bit 'for fun', like going around a corner on a city street, or in a parking lot where there were no other cars around. It still very much scared me, because being a passenger, I had no control over the situation and I would sort of have that flashback feeling." I would ask him not to do that, and then he would try to play it like it was an accident. Sorry, I know it wasn't. Finally, I blew up at him and said "Listen, when you do that, it may be fun for you, but it SCARES me. I don't care if you get it or not, but it SCARES me. Why do you keep doing something that you KNOW SCARES me? Why is that FUN for you? If you need to do that, then let me out of the car." I was in tears and everything. I think he finally got it enough to cut it out.