Funnily enough, this is one of the rough edges of English. It's not a natural phrase. Any English speaker will also sound awkward trying to make this phrase work. What I can tell you is this: 1. "in my wedding and Jack's" is dead wrong. Sounds terrible to an English ear. 2. "my and Jack's wedding." might work but sounds awkward. 3. "A wedding of mine and Jack's" is wrong. I think the average English speaker would say number 2. But honestly, they'd try to just say "our wedding," assuming the listener knows who you're marrying. I think this sentence would easily take just "my wedding" or "our wedding" and it would be completely acceptable. There's not always a convenient and natural way to say something. In English, expressing co-ownership over an object by two nouns is definitely a little rough. "Jack and Jane's wedding" works, but "his and Jane's wedding" feels a little wrong. "My and Jane's wedding" just sounds very wrong to me and I don't know how to fix it. I suspect the same is true of English speakers in general.

We would typically say: "..... a bridesmaid at me and Jack's wedding." ( grammarians get upset when they see "me" used this way, however it is perfectly legitimate way of using it, and has been used this way throughout our history. It also the most common way.)

Merlyn is right that many native speakers will say "me and Jack's wedding," and in conversation, this is almost always fine, unless the situation is very formal. You shouldn't use this form in writing, though, unless it's just a simple text message or something. Most native speakers know that it's wrong, and they'll notice it in writing, even though they may use it in speech. Unfortunately, I've got to agree with Michael -- there is no truly non-awkward way to say this in English. :P

Actually, the person would probably say: Jack and I are getting married. I want you to be a bridesmaid at our wedding" (or "at my wedding"), thus avoiding the grammatical problem.