Family and delivery room

Need to vent- So my mother and father ended their relationship very rocky (they were divorced by trying to work on things and she was seeing another guy at the same time) she is now engaged only 2 months from being involved with my Dad. Her fiancé is nice but she keeps saying my daughter will call him "papa" I've only met this guy 4 times.... she stated to me she wants to be in the delivery room but will leave right after with her fiancé if my Dad is there. I immediately told her that is not right and makes me feel she's just there for the show so she said she would stay but with her fiancé there too. I don't think this is right. My father deserves this time to meet his granddaughter for the first time and the rest of my family to meet her hold her, which my mom should be present for as well. I do not think her fiancé has a place coming in soon after to hold my daughter and also this would take away from my dad's experience. How do I nicely tell her I would like for him to come after my Dad leaves? I feel if she can't be in the delivery room and hold her pride aside for an hour or two with the family to meet our daughter and celebrate her little life I don't want her there at all. I don't think her fiancé has a place when the family comes in for the first time.