I'm with you, OP. It's been just you and your daughter for a very long time. She's seen you working really hard and I'm sure you've been a fantastic example to her.
And now you've achieved something you probably never dreamed you'd achieve - the highest qualification in the country - and your daughter isn't willing to shift herself to attend.
I, too, would be hurt. There are 70+ festivals in the UK every year. You will only have one PhD ceremony.
If you ask her and she agrees, it won't be the same. It's a shame your ex is such a twat and doesn't appreciate your hard work. Lovely for him having the fun side of life with your daughter, eh? I'm sure he was a great help with her homework, washing, ironing, cooking, taking care of her in the evenings, etc. He would have been the ideal person to tell your daughter how important it is for her to attend. What about your partner? Would he speak to her?
The problem is that if someone else speaks to her, it won't be the same as if she came to you and said that of course she would be there.
It's so bloody hard having children at times.
Congratulations, anyway - what's your expertise? What will you do once you've graduated?