Glad the rig is fixed!
Consider the human anatomy of a face, and how your own jaw opens and closes. There is a hinge joint, or point of rotation, around where your jaw bone meets your skull yea? Kinda like a door rotating on hinges, your jaw has a point of rotation.
If you look through various head rigging tutorials, you can see that on average there will be a neck joint, a head joint, and an end joint at the top of the head (all of which you have already!) - but they also include a joint in the center of the head (front the front view) that is located roughly where the jaw would rotate. From that new jaw joint, you would connect the end of the jaw which is actually the joint that you already have, located around the chin area.
In your file though, you already have your model skinned to your skeleton. So if you wanted to add a joint for your jaw or re-make the head setup, you would first need to unbind the skin.
