With rescues, I understand their policies because the pups have already been through so much. The rescue wants to be extra cautious.
For breeders, I also understand their reluctance. Some have a "no kids" policy, others will evaluate families individually.
I agree that kids aren't the only ones who drop small dogs (Kathy Lee Gifford dropped a puppy live on national television
), but kids tend to move faster than adults and have less motor control, tend to be more grabby, and rougher (although adults can be inappropriate too). Protecting a dog that has legs the size of pencils and a tiny neck can be tough and requires close supervision.
Most Yorkies don't have the structure or personality suited for bear hugs from toddlers. Kids are more apt to inadvertently taunt dogs, and I think this is risky for the kids and dogs.