hmmmmmm. I wonder if we put our human emotions on dogs and think they don't trust when actually they are just less needy than other dogs?
I have had 2 yorkies and been around many others and it seems like the more "cuddly" they are the more anxious they are in new situations. They seem to bark more too? ugh
My friend has a 13 year old who is tiny and adorable and never liked to cuddle. She loves her purse and my friend has always been able to take her everywhere with her. She just settles down alone in her purse and you never know she is there. Her other dog, the more social, "loving" one, couldn't go anywhere. She always wanted to be out seeing what was going on and barking for attention or control.
I love having a cuddly dog but I would give up a little cuddle to have a less needy dog. I really can't take my dog anywhere without major problems. I still try and yes, I have socialized her since she was 12 weeks old. She is only 13 months old and wants to kill everyone that moves towards me. It's a real problem.
Is your dog a barker? What happens when you take her places?
To get her to sit in your lap find a long lasting chew that she can only have while you hold it. Bully stick, greenie whatever. Good luck. I will trade dogs with you if you want.

kidding.