Welcome to YorkieTalk.
I have had kittens and I don't know how to explain, but Yorkies can be much more fragile (this is coming from someone with "large" 7 and 8+ pound Yorkies). I have to do the "Yorkie shuffle" even with my big boys for fear of stepping on toes.
Depends on your kids and what they want from a dog and how they would behave with the dog.
I would also consider how the Yorkie will fit into the busy lifestyle that most homes with 3 kids have. Yorkies need lots of physical and mental stimulation. They are very social animals and don't like to be left home alone for long periods of time.