You will have to be very patient if she has had a traumatic past. Be consistant, and have a regular routine. She needs to know what is going to happen, and when.
Once she realises that certain things (mealtimes, cuddles, bedtime, walks etc) will happen at certain times, she will soon start to relax.
Its good that she will let you cuddle her so she can be reassured you won't hurt her.
Maybe let her get used to you before you try walking her, and i agree, it must be a harness. Yorkies need to have a harness rather than a collar, and if she is frightened it is far too easy for her to slip out of a collar.
At 3, she is still very young and i'm sure her playful side will appear as she relaxes.
A really good site is fearfuldogs.com where you can get some helpful ideas and help, altho i'm sure there will be lots more advice on here before too long.
Good Luck, and let us all know how she gets on.....and of course, we need lots of pictures too!
