Would you invite someone to your wedding who had been rude to you in the past?

Of course you don't have to invite her! As people have said many times, with weddings there's always the risk of "offending" someone. You shouldn't ever have to justify who you invite to your wedding, and in a case like this, that's even more true. If someone chooses to be offended, that's on them, not you. I wouldn't even be considering inviting her.