My DB was with our GM when she died. I was at work - three weeks into my first graduate job and had moved away from home. He'd have been a teenager rather than 11; I think he was a bit shaken and subdued that evening, but absolutely fine the day after and, I think, quietly proud he'd been there. Her death had been expected for a while - no illness, just old age in her 90s, body gradually getting weaker and giving up, sleeping more and more and then just stopping breathing. So nothing traumatic. I think the shock for my brother was the realisation that this is natural; hard for a teenage boy who thinks he's immortal to come to terms with.
For DB, I think the pride and acceptance came fairly quickly as he was the one there - I had always been the dutiful one, visiting her in the home most days after school, phoning from university, coming back for weekends to take her out for trips, etc. It gave him great quiet pleasure that he'd been able to do something mature, responsible for her.
(No, I don't feel that I should have been there - I did what I could when I could, it so happened that it was DB's turn to be there for her, and TBH, I'd probably not have been the best person at that time, DB is a lot calmer and less emotional than I am! Maybe your DD was the best person for the job too, and her GGF felt this?)
Maybe, if appropriate, you could ask her if there's any way she'd like to remember him? Or have some input into the funeral in some suitable way - choosing the flowers, for example? I was a similar age when my GF died and was encouraged to choose flowers - it was helpful talking to my parents about which flowers, which colours I was choosing and why I thought GF would like them. Lots of stories that evening.
to both you and your DD.