Annoyed and about to call the baby shower OFF!!

Mo
So my fiance and his baby mother have a good relationship. They co parent well with their 10 year old son. We are currently 6 months pregnant and planning to have our baby shower in July. His baby mother wants to come and I don't want her to come because we don't even speak to one another. This fool really arguing with me about her coming. Talking about she is the mother of his child. Okay but she is not my friend nor is she our child's mother so that is irrelevant. If we were friends or cool at least I honestly wouldn't mind but since that is not the case I don't want her invited. Am I wrong? And I'm offended that he would even say to me if she can't come then it won't be a baby shower. Granted he probably said that out of frustration but dude I'm your freaking fiance, why don't you just respect that I don't want to invite her and let's continue on with our guest list. I'm super annoyed now!!!! He doesn't get along with one of my cousins that I'm really close with and I'm not inviting her for that reason. I don't want him to be uncomfortable at our event for our baby girl, why can't he think the same way?