I don't know your birds' history, however your statement,
I put Harper in the cage with Tennessee tonight and Tennessee puffed up, did the head bobbing dance while squawking. Then she was pecking at Harper's head and beak. And then she started to climb on top of Harper!
makes me think perhaps this is their way of bonding/mating? Budgies head bob when they are excited and they get on top of each other when they want to mate. They sometimes dance to attract a mate, and squawk for multiple reasons. They peck at heads and beaks to preen, feed each other, and bond. Unless they are pulling out each other's feathers or fighting more than little squabbles here and there, they are probably doing what birds do and behaving normally.