Beth at Anne's - hula hips = improved down transitions

Today was my first of two days with Beth at Anne Appleby's.  It was one of those lessons where it was "ah-ha" moment after "ah-ha" moment, making me nervous that I'll forget them all on my own.  I wish I could ride with Beth every week, because I get it, but then I'm afraid I'm practicing it wrong and making it worse in between.
I had three issues for Beth, but got very good insight into right circle issues as well.  My issues were Charlie wagging his head at the canter, down transitions from the canter to the trot, and stretchy trot circles.
We started with the walk, and getting a nice connected walk, but allowing the movement to come up through my hips instead of forward and back through my back.  This was really hard for me to get.  I put my left hand on my stomach, with my thumb on my ribs and my pinky on my hip, and the goal was that the distance would stay the same instead of scrunching closed, lengthening open.  It is like a slinky going back and forward with your back (wrong way) vs. hula hooping with your hips (right way).  When I hula hoop, Charlie can lift his back up into me, and I am more deeply seated, and also my legs can move with him. This isn't just in the walk, but also in the sitting trot. 
Beth said she can see a big difference in my swishy seat, although it came back more strongly as the lesson went on.
So we started with the walk and trying to shift the movement from my belly forward and back to hips up and down.  Then we went to a stretchy circle at the walk, and focused on feeling the "round" Charlie underneath me (the "poof" in his shoulders, which means he's stepping up underneath himself with his hind legs), which required slow, gradual letting the reins out, not flinging them away.  I had to ask him to tuck in his nose a little bit, but if I didn't expect immediate results, I got a much better stretchy walk.
Then we did trot work, and it is easier for me to keep Charlie round and connected on a circle than on the long side.  I had never noticed this, so it was really good to have Beth point it out.  If I pay attention, I can feel him go a little flat, and then if I do another circle, we reengage.
Then we did some trotting at the sitting trot, and I had to start slow, but then gradually work on building that trot up to "normal" speed.  I can control the tempo with my hips, but I have to be careful not to get tense, and I need to try to sit back just a little more so that I can use the flat lower part of my belly more powerfully.
Then we did some stretchy trot work, and I am basically just rushing it.  I fling everything away and expect him to do it perfectly, and what I need to do is 20%, then another 20%, then check in, then another 20%.  Then, once he gets it, I can speed up.  But for now, it is keeping the connection and making sure he goes down round and not out and flat and racing on his forehand.
Then we did canter work.  A down transition is really the same speed between trot and canter, it is just using the outside rein to say "here is the new gait".  This was really, really useful to hear.  And - fascinatingly - the right stretchy circle at the trot and right canter are the same issue.  It is still really different to go left and right, although on an entirely different level than last year.  I kind of fall apart and get all twisted, crank Charlie's head to the right, and he is also kind of lazy about pushing off of his left hind leg, so it is really not as good or easy as going to the left.  I have to remember to twist my spine a little left (my left shoulder gets further ahead than my right one), put weight on my right stirrup, and think about the rectangle and push my left side into the inside of the circle.
Charlie got pretty sweaty and was not forward enough in the canter, but it was hard because he would lift up into it but then kind of just stall in the air.  So I need to work on the correct feeling there.
This written version doesn't do the lesson justice.  I was like "OH!  That's WHY that is happening!" over and over again.  And - for the first time in a while, I started to see the next step up. 
It is great!  We are progressing.  There is still a long way to go, but we are so much further than where we started.  And Charlie is a real trooper.  Some of this is hard work for him, and he is a little less honest about offering it when I do it right, but once I am firm and say "this is what I want", he changes and shows me whether it worked or not.  He is such a good boy.
Next step is tempo.  Beth said it is a real eventer issue - we want to tear around going too fast, and I need to distinguish speed from impulsion.  I can feel it when it is up in his shoulders, but I can't always tell if things are too slow or too fast.