I'm going to invite my friend's ex to my party
Why would you invite your friend's ex to a party?
Because I have a really good time with them.
I understand why you might like your friend's ex, but it's not inappropriate to invite them to your party because it will probably upset your friend. I think you should consider your friend's feelings and not invite this person unless your friend is okay with it.
I'll invite her if I want to. I don't care about all that other stuff you mentioned because it isn't relevant to me anymore.
I could see why you would want to be around people you have fun with at a party. You should take your friends feelings and consideration and understand this will probably hurt them. There is the possibility your friend is no longer affected by his ex-girlfriend and you should try to talk with him about this.