Hey, Betti is an ear flapper, too. We started obedience training for her at a place called Diamonds in the Ruff. Lou and Greta were trained the traditional way...with choke collars and correction. DITR trains with clickers and rewarding positively. It is best for Betti since she was so shy of humans.
Anyway, one thing the trainers there say is that dogs have certain non-verbal cues, of course, and that the shaking, they call it "shaking off", is a behavior that means they are letting go of stress. So, in class we often see other dogs who are nervous at first shaking off and then lying down as they are more comfortable. Another behavior they display when they are content is yawning. In class they taught us that if we, as humans, demonstrate the yawning behavior it will actually help calm our dog. So, it is funny in class to sometimes see people mock yawning. Interesting concepts.