It's your fiance's wedding as much as it is yours and she can't expect you to dictate his guest list! Promise to sit them as far away from each other as you can and that's just about all you can do.
Explain it to your cousin calmly - she is probably terrified about seeing her ex but if she is reasonable, she will understand that this is how it should be. Sort it as soon as possible and then you can concentrate on the day itself.
Tell her she has to act like an adult and understand that everything is not about her--especially your wedding. Moreover, your soon-to-be-husband can invite whomever he pleases to the wedding and, because this guy is a friend, he may show up at your home every once in a while. It has absolutely nothing to do with her and she needs to decide whether she can be happy for the two of you or whether her own insecurities prevent her from attending your wedding.
It's your wedding , you can invite who you want, if she can't bear to be in the same room as him that's her problem not yours. I know it sounds hard but it's the only way to treat these situations otherwise your big day will be ruined by this sort of stuff. The only compromise of sorts is if you're having a day and a night "do" then you can invite them separately, but remember not to give into any emotional blackmail. Remember ITS YOUR DAY !!!