I can't give you an example of dominant behavior with humans, because I don't believe that dogs try to dominate people. Dog-dog interaction is very different that dog-human interaction. The behaviors you are describing are adolescent, unmannerly, rude behaviors. Not dominance. A dog running through a door first is a rude dog that hasn't been taught not to do that, not a dominant dog. Adopting a policy of nothing in life is free (NILF), working on place, structured walks, impulse control - all of these things will help. Exercise, both mental and physical will help. Tiring a dog out mentally is often more important than tiring them out physically. Can you tell us what your daily routine is with Lady? How do you correct her when she exhibits behaviors you don't like? Honestly, you've already tried to rehome her without her doing anything suspect. Teaching impulse control is a long process that requires patience and likely the help of a good positive reinforcement trainer. If you are looking for your adolescent dog to be a model citizen quickly, then perhaps rehoming is the right choice, because that's not going to happen. I feel like Lady already has a few strikes against her in your eyes.