I meant *granddaughter. He is grandpa for a reason. A great one at that.
I will stop with my headcanon that he is Kate's (or even Emilyko's) grandpa and he just loves his granddaughter so much and spoils her, letting her do whatever she wants when he is not sipping tea (or is it coffee) on the 3rd floor. And the other four are the crazy aunts and uncles.
It could be true. While I was leaning more on what if Kate and Emilyko are the twin children of a couple (two shadows that had undergone unification) from the shadow house and somewhere along the way the family was separated. The couple could have successfully run from the shadow house or they could be from the direct lineage of the Great Grandfather and had more privileges to go in and out of the shadow house. We can only speculate until the grand reveal.

So is it safe to say that Emilyko met Kate before she entered the shadow house?
Is the shadow our beloved Kate-sama or another "Kate"? Then how did she get in the shadow house or out of it if shadows are only linked to the shadow house and the in and outs of the shadows especially children are restricted.
I can only guess she is a free shadow not linked to the shadow house. If she had been in the house she would have been monitored and remembered by the rest or at least some older shadows or someone.
Also, she had luggage with her as if she were travelling or running from something. She has to have been living as a shadow imitating a human for some time. I understand Emilyko borrowing her name but why would she give Emilyko her clothes? Was it just good will? Or was there a plan?
Then the plot twist of all this was the thought she is the Great Grandfather's daughter and she wanted some time out of the mansion and grandpa being the "great grandfather" he is let's her out to see the world (or just mirrorside) and then Kate meets Emilyko, her world, and we find ourselves here.
More of me writing too much again.