I believe you're right. I had a friend who is a vet tech and dog trainer suggest that it sounds like fear, but I disagree. I think it is dominance. I'm not sure how to stop it, or identify it, but here is why I have concluded dominance.
Thor goes out of his way to stand over Taco's head. Taco could be sleeping, and he'll walk over and just stand over top of him. He also tries to be first into rooms, higher up than everybody else, etc. I'm working on this by making him work for everything. He's very receptive, and he sits before we go out doors, and waits for me to call him, etc.
When we visit the dog park, I think it's sensory overload, and you can't tell him anything. He will strut up and down the fence at dogs or people on the outside of the park, and again with the dominance, treats the dog park like his own. I go with both of the dogs, and I will keep Thor leashed, and Taco will play with all the other dogs. I make Thor sit between my legs, and watch. He used to bark at the other dogs, and we've gotten past that. I would let him off the leash, but I guarantee he would run right for the first dog in his line of sight and attack it. Even dogs that submit, he paws at them and tries to flip them (or maybe just a rough player?) There is one dog that he gets along with, a small Frenchie. The frenchie is also deemed a rough player because he's very vocal ie. barks and growls, etc, but him and Thor play great. Thor also will lunge at other dogs if they come close enough, after seeming like he was calm and collected.