If you want to attend a wedding in about a month, you need to string them along for a few weeks.
Tell them you and/or your wife are distraught because of her suddenly being added to the lineup and you need some time to think and get over the shock and the headaches. It doesn't have to be a good excuse, just insist upon it.
"I will gladly meet with you all, I think she will too. But this is so sudden for her, she needs time. You brothers know about them being the weaker vessels and all." Then drag out her time-of-the-month or doctor's visits or anything related to emotions that they will be afraid to combat. See if you can get 2 or 3 weeks out of that.
Add in that you will need another week's notice to arrange for the time off for everyone, you and the wife and your witnesses. Call back and say the first time they asked for is no good, "....perhaps the following weekend."
Then do the appeal stuff and it should pass after the wedding.