Yorkie's tend to be very delicate little dogs, especially as puppies. My Suzi is so much like a toddler that it is a lot of work! If your little children are calm then it would be easier on your family to have a small dog. However, most 4 yr. olds are busy, little people who can't understand why they could not handle a puppy like a stuffed animal.
You might want to consider a rescue Yorkie that is already full grown and calmer for your kids. Some Yorkies are bigger and more robust the others too.