OP, I see you haven't been back but I hope you will consider what most people have been saying. There are a lot of wise people on Mumsnet. Sorry for the long post here but I hope it may give you food for thought.
In my own case, my mother is toxic and I have been advised here to go no contact with her. She is in her 80s and I'm sorry I didn't cut her off many years ago. I see some parallels in your attitude and am posting in case you might consider opening your mind and hopefully moving on from this small incident towards a more positive future.
My mother, unlike you, never brought my children to school, in fact she never helped me in any way. That's ok, grandparents aren't obliged to help with their grandchildren, however she didn't understand that criticising my parenting, and criticising my children, is not acceptable.
You are helping your DD and hopefully she appreciates this. As a parent yourself, you know how much children change over the years. Look to the future rather than getting hung up on something that happened over the space of 5 minutes.
It is ok to talk about how you felt, for example "I didn't hear you say goodbye and then I didn't know where you were so I was very upset and worried, and cross too because I was worried". But to go and tell your child that her child is rude will help no-one. Effectively you are criticising your daughter's parenting and creating a distance in your relationship.
Because I was brought up in a severely dysfunctional, toxic home, I didn't understand that it was not right for my mother to criticise me and my children, who she saw but rarely and didn't actually like children. I tried for years to keep her happy but regularly felt I had to protect my children from her criticism. Always she told me they "should" be doing this or that, or they were badly behaved and I had to accept this. If they didn't behave exactly as she decided they "should", there was hell to pay.
Now they are adults and she has no relationship with them. She recently told me that if I had been a proper mother she would have a good relationship with my children, I posted here about it and got the advice to walk away.
@BlossomOnTrees it could be you are a wonderful grandparent. But some of your comments concern me -
AIBU to have told DD this was rude of my granddaughter? Tell your DD you felt hurt, not that GDD was rude. Stop judging your grandchild which is also judging your DDs parenting.
Granddaughter is developing an attitude. She has just turned 9. Don't be like my mother who refused to examine why my children may have had an issue with something. She just put down their behaviour without seeing what might have driven it. Express your feelings, not your judgement.
She was in a bad mood as she gets angry when people do not do exactly as she wants. Chip off the old block then.
She may well have said goodbye but I don't believe she did. So you are basing your judgement on something you are not even sure of.
Tread carefully. My mother is going to die a bitter, poisonous old woman. It could have been so different if she had opened her mind.