Sorry to hear your having problems with Billy.
I am having similar problems with Betty, although with people (strangers), rather than dogs.
She too does the freeze thing when people approach her, then when she realised she didnt like the smell of them she'd lunge into a barking fit. It seemed to be getting worse, almost as though she was getting 'braver', and I didnt know how to handle it, so I saw a behaviorist for help.
Basically, Penels saying the same as the behaviorist, she was taking the mick out of me! I live with her, she takes me out for walks, you get the idea!
First step is to be the boss! Make him sit and stay while you walk through the door ( every door!) first, then call him through to follow, has to be invited to join you on the couch, if you allow it, you have to eat first, pretend to eat from his bowl.
This may all be sooo obvious to most people, but I didnt know that letting Betty run ahead into the house and other things like that made her think she was top dog...cheeky mare!
Its a real pain to stick to it, it takes about half an hour to get to the kitchen sometimes! I too sometimes feel nervous when im trying to get her off the couch when she's just jumped up on it, when shes got that stuborn look on her face. But you have to stand your ground, I do believe they can sense your feelings
Sorry for rambling on havent spoke about Bettys probs before. I'll be really interested to hear how you get on with Billy.