Toto did the same thing .... would just flatten herself out on the floor and lay there! We eventually found a private trainer in Louisiana [a Dog Whisperer] who came to our home and within an hour had her prancing up and down our driveway like a showdog!!
I have no idea what he did but she has walked perfectly on the leash ever since. Please don't give up and please, please don't use a collar. The Yorkie trachea is so tiny and delicate it can be injured very easily.
The other reason to use the harness .... we went through a horrible week after my daughter's Westie was frightened by the UPS truck and pulled his head out of his collar and ran! She couldn't find him and long story short, a lady rescued him from the middle of a busy highway after he was nearly run over by a truck. Ultimately she got him back and I dare say, she will never ever take him out on his leash without his harness!
Good luck and please don't give up on your little one!