Sweaty butt (for Duke)

Our dressage lesson today was similar to the start of our jump lesson from Thursday, but was much harder.  And equally difficult to translate.
When I rode Friday, after the lesson, I remembered that one of the things John told me to do was to send Duke forward and back within the gait.  So if he was trotting, to slow him down to almost a walk, then go back to regular trot.  We did this at both trot and canter.  We did it again today.
We started with five minutes of trotting (I had been sitting around laughing) that John said was just throw away work - not to worry about getting him round, but just let him trot and loosen up.
Then we started working on a 20 meter circle, with a few changes of direction.  John did minor corrections here, a little more bend, a little outside leg.
From there we moved onto a smaller circle and John focused more on the precise aids - outside leg now - now - now, outside leg back, leg yield him out of the small circle onto the larger circle without changing my hands, taking up my reins (they slide out long and loose) - not looping the rein when I give, but just giving a little - but giving a little whenever he softened.
A few times we had to counterbend and then come back onto the correct bend, and then he had us switch sides of the arena and work on the right side.  Here, he had us working on a 10 meter circle, and then he had me canter on the 10 meter circle (as Duke's first right lead canter for the day!).  To my amazement, Duke did it.
John tightened Duke's noseband, which I have been leaving one hole looser, and he said that leave at least a hole for the show.
Duke had sweat under his chin and foamy sweat in his butt, but he seemed relaxed and happy.  He's a good worker and tries hard.
I could - sometimes - tell what John was about to say, and I tried to use my "cross" aids (inside leg to outside hand) without John having to say it, but it took a lot of concentration just to keep up, and I'm not sure that I feel yet when I need to give the aid.  I can feel the difference, after John tells me to, like I can feel when I put my outside leg back and use it with the beat of his steps, how he gets round and soft in the bend, but if I was just trotting around by myself, I would never think "oh, now is when I should move my outside leg back".  I am hoping that with time, this will start to sink in, but I imagine that whenever we start something new, it must be kind of frustrating to teach me, and just watch me struggle and struggle and struggle until I finally get it.  Please, please, let me get it.