I don't think I'm going to invite my brother's gf to my wedding
What happen that you would not want her to be there?
I can't stand her. There's no reason for me to invite her.
You can invite whoever you want to your wedding. It is your event. If you can't stand her, don't invite her.
I don't want her to bring nothing but sour grapes to my wedding.
You should probably see if your brother is cool with it. Since it is your wedding, he will probably understand and accept your request. Either way, I support your decision and hope things will work out smoothly for you.