Research is wonderful and talking to other yorkie owners to be admired. Since both of our yorkies were grown when we got them, I can't say how they were trained as pups. Where they socialized? We don't know. Our smallest yorkie, weighing in at less than five pounds, tends to snap with teeth like razors. He is a rescue dog and was removed from an abusive situation. Maybe it is a trust issue...maybe it is just his personality. We trained our grandchildren not to approach him. If he wanted to be around them, he would approach them. They also learned never to touch him if my husband was holding him. Shucks, I learned never to touch him if he was being held by my husband. That is his human and he is highly protective of him. Strangers are totally another problem. Because he is so little and so cute, they reach down to pet, sometimes with these words coming out of their mouth, "Does he bite?" (Advice: Ask BEFORE you start to pet.) My reply is, "He might."

However, with this being said, he is a very sweet and loving dog. We just have to be aware of how others approach him.
We also have a larger female yorkie, 9 pounds, also a rescue, that came to us grown. When someone arrives at the house, she barks and charges them. We have made progress in training her not to do this but she still has some work in that area. Our grandchildren know that she does not bite and will settle down once they are in the house. She and my grandson became big buddies on a vacation trip. However, we have never witnessed her around toddlers. She is not a biter but think she would become nervous if they squealed and ran at her.
Like humans, dogs' personalities are different. If you have any doubts about its interaction with your grandchildren, you might want to think carefully before purchasing. There are so many dogs that have been given up by families because they weren't willing to deal with issues a pet may bring into a household. You also might consider a rescue yorkie that has lived in a foster home. The foster parents know how their foster yorkie interacts with children and if it would be a good match for you. If you need a suggestion to an organization that fosters yorkies, please contact me.
I am not trying to discourage you from getting a yorkie. They are wonderful members of our household and don't know what I would do without them. Again, good for you for doing research!