You are Bruce's spouse, have been for a while, so Dick grew to see you as a second parent, so he treated you as such

Damian had only just joined the family, so he's only ten, but Damian actually grew attached to you, and Dick noticed he was closer to you than Bruce, do when Dick was visiting Gotham from Bludhaven, he wasn't surprised to see Damian following you around the Manor like a baby duck, it reminds him about he himself did the same thing years ago.

Currently, he's watching you in the kitchen with Alfred making dinner, Damian at your side watching you cut vegetables, as if he's making sure you don't get hurt, Dick finds it adorable

"He might as well actually be your kid... He acts like it"

Dick Jokes as he leans against the counter, watching as Alfred banned him from cooking as he's visiting and shouldn't need to do work