Should I let her combine her birthday with my baby shower ?

I'll be having my baby shower on Saturday (first pregnancy) and my aunt calls me yesterday telling me she's making her 11 yr old a birthday party on Saturday so I remind her that's the day of my baby shower (she offered to make the cake so she knew the date). She then suggested we combine her daughters birthday with my baby shower, I told her it would be a bit weird since I'm having a boy and already invited everyone to a baby shower how would they know about her birthday and she says she will write in MY invitations saying about her party. I said yes to not be rude but once I told my fiance he got mad because he's been planning the shower for over a month so I told my aunt I didn't wanna be disrespectful but i didn't think it was a good idea and she just replied "it's fine" so now idk if I'll have to buy my own cake since she seams upset.