I would look for a new trainer. I live in a small town too in California. Most of the time I have to go to a couple cities outside of where i live for services. If your not comfortable with the trainer in your town, look around. I am sorry about what happened to your other dog. However, it was biting, and hurting children/you. It would not have been long that animal control would have taken that dog.
Yorkies are very smart little dogs, and with the propper training and consistence you will have no problems with your puppy. I would go to the Library, and research the breed, and training methods that you can implement on your own .