She is being rather rude here. Your girlfriend is right about Loki telling Luna that he doesn't like it and needs space. By the time you hear any growling or see air snapping, he has likely expressed through more subtle body language "Stop,"
several times. Which, when Luna essentially ignores
again, Loki escalates. When you see Loki give Luna "I'm done," signals, and you can tell Luna is going to persist, separate them. Not as a punishment, but as listening and meeting Loki's need for peace and helping teach Luna canine manners.
I assume you teach your dogs not to jump on you? Because if Loki already has this down, and sees Luna jump on you; well, according to the rules of the house, she's not listening to you either, is she? So, he's helping reinfore proper behavior. Of course, not all dogs police the behavior of other dogs, so this particular mindset might not be accurate here. It could be resource guarding with you as the resource, though if these are the only incidents, I don't necessarily think this is the case. Is there a way to separate Luna or the two farther from the door when you come home? It would give them more space and less body pressure, which should help with this bottleneck of sorts. Alternatively, you can teach them to go to mats and wait until you release them. Or, if you like enthusiastic greetings (I do), instead of having the greeting right at the door, you can lead them to a more open space first.
As Luna settles in and learns etiquette through maturity, training, and experience, and Loki learns he will get his space, a lot of this should resolve.
