Be very patient with her. Some dogs just aren't the social butterflies, but hopefully in time she will become more secure and enjoy playing with the other pooches. I agree with Miss Marley with her advice about trying not to pick her up every time she asks - just don't let her get too stressed out.
I want to commend you on being such a good Yorkie Mom. You are going to great lengths to socialize little Sophie -- please give yourself a pat on the back
.