Yes, yorkies can be extremely difficult to train, and each needs their own technique to get the training right. Rizzo has a very similar temperament to Alice in the shyness category and I've had to learn a whole new approach to training.
First, find a treat that she will go bananas for, Rizzo likes anything particularly stinky (jerky type treats for dogs or Parmesan cheese works well too)
Then you need to train her tricks that don't involve you touching her, like another poster said, just scoot your hand back until she eventually sits, praise and give the treat. Lower the treat until she is in a "down" position, praise and treat.
It's going to take a lot of work to get the shyness out of her, I'm still working hard with Rizzo and I've had him for a year now. I can take him for walks now without him just trying to run and hide constantly, but he still doesn't want to be touched by strangers and he'll bark if they get too close.
So find a training technique that works for both of you, bring in a professional if you're having too much difficulty finding it. They've seen a lot of dog personalities and breeds, I'm sure they could help you out better than us
Good luck!