There are some full moons when the dogs have no effect whatsoever and then there are some full moons when are extremely hyper, totally defiant, and testing your every move. PATIENCE! My clients have called me and said, “This dog is driving me crazy, he or she has not acted like this is a long time!”
I used to be a teacher and the full moon that had plenty of energy, the kids looked like little ants moving around the classroom. They had an internal motor that could not be stopped. Dogs are the same way!
The leash is your tool. You have control! When your pup is being defiant and putting everything in their mouth they should be placed on the leash, so they can not sneak off and get in trouble.
Training will definitely help. Even if you work with them for just 5 minutes it will help. The mental stimulation gets them more tired then just playing with their toys.