who is the head dog

neither of them is. you are the top dog, and you need to assert yourself, and make it clear that no one is fighting for top dog, as the position is taken. they are young, and sorting out their heirarchy, and this will likely settle, so long as you stay assertive, and stop any behaviour as soon as you see it's going to happen. you don't need to be physical with them to do this. a look or a light touch with a confident attitude should show them what you mean. you're seeing their intention to try and take themselves up a peg, in the early indicating body language, and you step in and tell them you're top dog, and you don't want your pack playing up.