I am not a trainer, however I have successfully trained several dogs of varing breeds. I would not use what he suggests on any breed large or small, there are so many more affective methods of training.
If he has not heard of the "trachea thing" then he has not worked with small dogs. I can not count the number of people that I know who own two or more females and have no problems. This guy seems backwards on so many levels. How frustrating his visit must have been for you.
I agree that it may be harder to train two puppies at a time, however it is not impossible. I think most yorkies do better with another dog, companion. I bet your girls will be great friends as they grow