I know the issue is really about wanting your DD to want to attend the ceremony. However, could you possibly consider this as a compromise: arrange a very very special party or meal out - with your daughter there - to celebrate your achievement, some days later - with your DP maybe making a short speech about what an amazing achievement this is.
Instead of sharing your success with the hundreds of other students receiving their certificates at the official ceremony, you would become the centre of attention and you DD would be a witness to this and hear from others who love you - eg DP and friends etc - what a massive achievement this has been. This would be your own special and unique way of celebrating, would allow your DD to be there without a 'conflict of interests', would really 'mark' the significance of the occasion. It would be YOUR PhD party and you could have a decorated cake/balloons etc emblazoned with your success "Dr...."!
If your DD were also able to invite some of her close friends along, it would make the occasion more teenage-friendly but also, sometimes when DCs friends are around, they kind of make DCs 'see' their parents in a better light IYSWIM? If her friends are saying, "Your mum is amazing, isn't she?" then she'll be feeling that even more, too (teenagers are so influenced by their peers). You'll have 'witnesses' to your success that are special and meaningful to you and to her - not just the anonymous crowd at the official ceremony.
Your DP could bring along your certificate too and hand it over again, with his speech. DD could be asked if she also wanted to say anything special to mark the occasion or read a special poem out or something.
You could then also use the opportunity to say a few words yourself, in front of all those who love you, about how proud you are and how happy you are that the support of DD and DP and friends made it more possible for you to pursue this success.
I know this side-steps the issue of wanting DD to be there for the official ceremony but as it neither seems clear whether it's right to say something again to her about it or not, this would be a way of you feeling proactive in creating a special and very personal way of marking, publicly, your amazing achievement.