Coach Stuart's blind assessment of my stroke was correct, the advises Dshen gave me was also good ones.
I was stalling sometime stalling my recovery at exit. My balance is also to be work on along with pretty much everything actually:
My kicks actually generate/start the rotation and one is weaker than the other one (/bad knee). I may try a 4 kick per beat pattern to see if it fit me. I tried to work in symmetry today 2KB and a breath every three strokes but it breaks often. I think when it does breaks or I try to push myself a little further I wonder if the pattern could actually work to my strength and also weaknesses instead of having the stroke breaking in not controlled manner as I inadvertently found myself breathing only to the right again and every two strokes.
As I work on the extension forward with my right arm, my body does not rotate as much as on the right side so I "swim less downward" as you would say (or put less chest pressure) on that side. I think it is the reason why my breathing on the left is bad: my center of gravity and of buoyancy are not in the same positions as when I breath on the right side.
My right shoulder blade is too lose (old injury I did not take care well enough) so it is more flexible (in a bad way) I can get more extension without rotating (than with my left arm), I can get into an "earlier" EVF than with my left arm. As I said yesterday it furthers throw my stroke out of balance ND I also realize today that as the shoulder is slightly further away from my core (/loose) I can't translate all the strength from the rotating core and its large muscles. Good news I can do a correct move but it requires a lot of awareness. I think I should see a physician therapist or osteopath and also do airborne exercises to make that shoulder more stable.
Those two reasons together explains why I'm more balanced and breathe better (both sides) while kayaking: shoulder driven rotation and stroke overall partly hide my lack of control and deficiencies in other areas.
Overall an interesting day at the pool today. I worked at slow pace and I think I increased my awareness of the issue with my stroke and my body as well. It is still a little frustrating to rework things I thought were improving (AND work at lesser speed) but I realize that (slow) front craw training can be turn into physical therapy as I grow more aware about myself.
I can do breaststroke to but I will have to have high awareness during the outsweep.
As much as I want to learn butterfly, I think I will have to stall my efforts at the moments, it is simply too easy to inadvertently try to force through the stroke and even on short distance I think it might hinder the efforts I have to do to stabilize my shoulder blade and matching muscles => I'm going to work whole body dolphin and dolphin kick and so "cobra" type of breaststroke in the mean time.