Thanks for the insight coach :)
Indeed I gave up on this approach. For the butterfly I realize I don't need, there is/was a massinve inefficiency in my underwater arm movements. I had pretty much no push. The catch was ok but then I was a little too careless with my pull which was setting for an inexistant push.
I understoo I have to work consciously my back muscles (romboide, mid and low trapeizus during the pull so I'm in a proper "shape" to efficiently push.
The lack of power during that face was clearly what was making my breathing complicated and so my recovery.
I've yet to postural work to do, to resist my muscular imbalance, so really relaxing prior breathing is too much for me at the moment, I can't focus on so many things. Yet I had 25/30m today at high pace it felt great, I could have continue but I crossed somebody and my breath was getting a little short too.
I think I've got the core of my butterfly dow today, I'm extremely happy about it.
As I was thinking about this lack of power during my pushing phase I wonder if it carried to my freestyle without me noticing... guess it did. As I tried to correct it I realized instantly that my body rotation was slightly ahead of my arm motion. Again quite happy about the finding significant gain in power with next to no extra efforts. As Dara Torres said in an interview"she tried to involved more muscles into her swimming" that is a great advice, a whole mbody activity, you share the load on lots of muscles and gain ahead room.