Of course, all of you know it. A world filled with light, people begin fighting, darkness is born and the world ends up being destroyed. But, the light remaining inside children's hearts rebuilt the lost world. Could Kairi's grandmother be referring to the Dandelions? Dandelions are children, after all, who will not participate in the keyblade war. She doesn't know the term "Dandelions" and so, in her story she is referring to them as children who rebuilt the lost world.

Was she born during that time or am I going crazy?

Yeah,  she probably doesn't know about the dandelions, but remember that Kairi's grandmother story is basically told as a fairy tale. I think the story of the keyblade war and the dandelions rebuilding the world has been losing more and more details over time, becoming a legend. So, she tells this story as a tale, and she shouldn't know the real events. But this tale has a truth in it, which is the story of the X series.

That's actually what I was thinking.

 

I mean it looks like it's following Kairi's grandmother's story.

 

The dandelions (the kids) was told by Ava not to participate in the war, but instead go fly into Unchained.

 

Cause if they DID participate in the war, and they don't make it out alive, NO HISTORY OF KEYBLADE WIELDERS? (of what she also said I think...). No chances of the worlds being reborn? No crazy Xehanort being evil?