With your children being 7 and 9, I'm sure there are lots of breeders that will consider it.
Maybe even a few rescues if you look really hard. Maybe look in the looks animal control shelters? I'm sure most of them don't care as long as they can get the dog out of there...
I know some breeders don't adopt to people with small children just because they have no way of knowing if they know how to handle a dog. then you have some breeders that will watch the kid(s) and dog(s) interact and then make a decision.
Some Yorkies do prefer one person in the family over everyone else and sometimes it is hard to get around that. Just make sure that the dog's care is always split between everyone (everyone takes turns feeding, playing, etc.).