It's always hard to leave them but grooming is part of owning a Yorkie. I use a home groomer and always take the 3 together that way they are not really alone. She super quick too and I usually have them back in a few hours. Just wait when you pick her up~she will be so happy to see you.
I do have a visual of you leaving snacks, blankets and toys for her~very sweet and shows how much you love her.
Don't worry yourself so much about socialization she is still a baby. Maybe you can join a puppy class or a meet up in your area. They both will provide excellent opportunities for socializing too.
I really like my home groomer and was able to find her through my vet. Maybe you could call and ask if they recommend a home groomer in your area. It's nice to be able to know your groomer one and one in a small setting.