Do you think Katrina knew that her daughter would someday find the secret of creating the color blue?

Possibly, she had faith in her daughter's talent and taught her everything she knew before passing on. She wanted to prepare her, Kira became adept in all of the things her mother shared with her. I have no doubt that her mother knew that if she kept learning she'd find the secret.

Thankfully, the Gaurdians to care of Kira after her mother passed on, and thankfully they knew her talent with the needle. All of these things proepared Kira.