My partner's father didn't go to his graduation ceremony but he did go to his daughter's. It is outrageous and whilst your reaction might be something you want to change later, it's coming from a very understandable place.
From reading your post though, I do notice that you mentioned your dad being willing to change his dates and that being the thing that cinched it for her saying you didn't need two parents. She may well have a very good reason for not being able to come or possibly not being able to come that she felt uncomfortable about. The thing is, from the sounds of it, you may have put her in the position where she ended up feeling like she was being compared unfavourably to your dad which upset her. I'm not saying she's right, but do try and understand it from her point of view if you can. You'll know better than me or anyone else here what that is.
If you want her there, you have to admit that to yourself and to her. If she she thinks you don't want her there, what incentive is that for her to come? Be prepared to sacrifice a little pride here, because it is your happiness at stake at the end of the day. It was an argument I doubt either of you wanted to have and there's no point in holding your ground over it now. It'll eat away at you if you do.