To OP, when I filled out the application for my dogs, I was sure to also include a list of refrences on my daughter. People that had worked with her and knew her but that I felt would be unbiased. The breeder liked that I gave child refrences, as silly as that may sound. And she checked them
I also let her know of the rules that we had in our home, for our first yorkie, and that they had been followed and very effective for a more than a year. I took a picture of Copper's "safe zone" and explained to her how it worked and that it was always available should he want a break. Or if I was unable to have direct supervision he goes in the "safe zone".
She liked how thorough that I was and then agreed to meet my daughter. Obviously your rules work for your house as you already have a yorkie. And you may or may not have a "safe zone"
but these were some things that helped the breeder better understand my family, and made her trust me with one of her special babies.