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I find that the palate / jaw mirrors the rib cage, if anyone else has a canted occlusion. Due to human beings tendency to be right handed; have a stronger right diaphragm (lower and extra attachment on lumbar spine); and a heavy liver to anchor the right abdominals; the right abs are strong and the left side weaker. This tends to internally rotate the right side (closed down) and the externally rotate left side (open up). This can be mirrored in the occlusion, with a more resistant right side , and left side expanding easier. The opposite pattern can exist, but it is less common.

In general, it is ideal to have the right side palate wider than the left to offset human asymmetry. In other words, we should strive to externally rotate the right temporal bone (palate) , and internally rotate the left. This can help offset our inherent asymmetry.

Check out great post by Apollo detailing that perfect symmetry is not the goal, but functional balance within our asymmetrical structure. 

Learning to fully exhale with left ribs and inhale into the back with the abs on closes down the left side, and allows the right side to decompress.

Here is the PRI Hip Lift that helps to do that. I found my right side palate expands easier with this technique.

PRI 90/90 Hip Lift.

1:  Laying supine with your feet on a chair in a 90/90 position, head supported with a pillow.  Your abdominal wall should be relaxed and as soft as possible.  Ideally you would use something like a small ball between your knees to squeeze and keep your legs from rotating out.

2:  Feel the back of your heels in the chair and press them down to engage your hamstrings (back of your legs), lifting your tailbone slightly off the floor and fully rotating your pelvis posterior, tail tucked under. 

3:  Exhale gently, allowing your sternum to slide down toward your pelvis with your lower ribs flattening along the floor.

4:  As you attempt to exhale more fully, engage your oblique abdominals to expel the air completely, pulling your ribs and belly down toward the floor (think of the A shape from your sternum to your outer hips, and the V shape from your pubic bone to your outer hips drawing together.)

5:  Allow your neck to relax in to a lordosis as you exhale (head tipping back).

6:  Pause for 3 to 4 seconds at end of your exhale.

7:  Maintain this abdominal contraction as you as you re-inhale down through this contraction into your pelvis and sacrum.  Do not allow your front ribs and pelvis to pull apart at all.  Air will flow into your back and your inhalation will not be that deep.

8:  Exhale more fully, ratcheting up the abdominal contraction and rib ‘flattening’ position. 

9:  Repeat for 3-4 total breaths.