Your friend didn't say if the child lives with them or his mother.
You are dating a Baby daddy, you should know that the other woman will not just disappear. She will always be the mother at functions like this, while you take the back seat. So it's important to always ask your guy before and during preparation where the woman comes in and give her the space she deserves.
Were you thinking of replacing the mother when you were renting bounty castle?
Are you sure your boyfriend does not want you to attend, or you won't want to be laid back at the party while the child's mother takes the front seat?
It's your decision if you want to cancel some of the things you ordered, but don't cancel the cake. Let your man know that you were presumptuous in making those preparation without asking for the mothers position in the whole thing. Don't leave him based on this incident. He also might not have factored the woman in initially, but his attention might have been drawn to it and he may just feel the right thing to do is have the woman there. And we don't know your relationship with the Baby mama, he may feel it won't be good to have you both together if you've not been particularly cordial.
We don't have all the picture, but you do, so make your decision based on everything, not just this single story.